IMBSIR 75-779

The Development of an

Improved Compression Test

Method for Wall Panels

C.W.C. Yancey

LE. Cattaneo

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

December, 1975

Final Report

Prepared for Division of Energy, Building Technology and Standards

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D. C. 20410

NBSIR 75-779

THE DEVELOPMENT OF AN

IMPROVED COMPRESSION TEST

METHOD FOR WALL PANELS

C.W.C. Yancey

L.E. Cattaneo

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

December, 1 975

Final Report

Prepared for Division of Energy, Building Technology and Standards

Office of Policy Development and Research

Department of Housing and Urban Development

Washington, D. C. 20410

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

James A. Baker, 111, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Table of Contents

Page

SI Conversion Units

Abstract I

1. Introduction 1

1.1 Background 1 1.2 Objective 2 1.3 Scope 3 1.4 History 4

2. Laboratory Experiments 8g 2.1 Description of Specimens

g 2.1.1 Wood-Frame Construction

g 2.1.2 Steel-Frame Construction

2.1.3 Fiber Glass-Reinforced Polyester Panels 11

2.1.4 Foamed Urethane Core Sand^-T-ch Panels 11

2.1.5 Paper Honeycomb Core Sandwich Panels 11

2.2 Loading Procedures 12

2.2.1 Test Load Reaction Frame 12

2.2.2 Loading Fixtures 12

2.2.3 Rate of Loading 12

2.3 Instrumentation and Measurements 13

2.3.1 Load 13

2.3.2 Deformation 13

2.3.3 Recording 14

3. Analytical Investigations 25

3.1 Load Distribution 25

3.2 Eccentricity of Loading 26

3.3 Statistical Parameters Needed to Describe Results 27

4. Discussions 29

5. Summary and Conclusions

gg

5 , 1 Summary

gg 5.2 Conclusions

6. Proposed Standard Method of Test for Compressive Strength of Wall Constructions 73

7 . Acknowledgements 86

8. References

gy Appendices

A. Computer Program for Load Distribution Analysis 38

B. Core Radius Calculations for Some Typical Wall Sections 97
SI Conversion Units

In view of the present accepted practice in this country for building technology, common U.S. units of measurement have been used throughout this publication. In recognition of the position of the United States as a signatory to the General Conference on Weights and Measures, which gave official status to the metric SI system of units in

1960, appropriate conversion factors have been provided in the table below. The reader

interested in making further use of the coherent system of SI units is referred to:

NBS SP 330, 1972 Edition, "The International System of Units"

E380-74 ASTM Metric Practice Guide (American National Standard Z210.1)

Table of Conversion Factors to Metric (S.I.) Units

Physical

Quantity

Length

Area

Volume

Temperature

Temperature difference

Pressure

Mass

Mass/unit area

Moisture content rate

Density

Thermal conductivity

U-value

Thermal resistance

Heat flow

To convert

from

to

inch

foot

inch^

foot

inch^

foot

Fahrenheit

Fahrenheit

inch Hg (60F)

Ibm

Ibra/ft^

2 Ibm/ ft week

Ibm/ft-^

meter

m

Celsius

Kelvin

newton/m

kg

kg/m^

kg/m^s

kg/m^

Btu/hr-ft -("F/inch) _W_

„ mK

Btu/hr-ft .°F W

'F/(Btu/hr.ft )

Btu/hr.ft^

m^K

K/ (W/m^)

W/m^

multiply

by

2.54* X 10"^

3.048* X 10

6.4516* X 10

9.290 X 10

-4

1.639 X 10

2.832 X 10

-5-2

t, = (V32)/1,

Atj^ = (Atp)/1.^

3.377 X

10"^

4.536 X 10

4.882

8.073 X 10

1.602 X 10

1.442 X 10

5.678

1.761 X 10

3.155

-1

-6

-1

-1

*Exact value; others are rounded to four digits.

XX
The Development of an Improved Compression

Test Method for Wall Panels

by

C. W. C. Yancey and L. E. Cattaneo

Abstract

An experimental and analytical investigation of the primary factors involved

in the testing of prototype wall panels under axial compression loading is reported.

The objective of the investigation was to develop a method of testing wall specimens

that incorporates the best features of ASTM Standard Method E 72 i-;hile at the same time incorporating improvements in the areas of deficiency in the Standard. Twentyfive laboratory tests were conducted on samples composed of five types of wall

panel construction. The panels were tested to failure under either of two different

eccentricities of load, while being supported with one of two types of idealized

end conditions. Selected test results and detailed descriptions of the laboratory

procedures used are presented. A computer-aided analytical study of the variables

affecting the degree of uniformity of loading was conducted. Equations based on

the analogy of beams supported on elastic foundations were used in the analysis.

A study of the statistical parameters commonly used to interpret test results was conducted to establish useful guidelines for predicting structural performance on

the basis of small sample test results. A compression test method applicable to traditional and innovative wall constructions is presented. The principal additions

in the revised test method are as follows: (a) a provision for variable eccentricity,

(b) a procedure for selecting a load distribution assembly which will be compatible

with the test panel.

Keywords: Compression; eccentric loading; flat-end; kern; loading rate; pin-end;

test method; wall panels; walls.

1 . INTRODUCTION

1.1 Background - This study was conducted as a part of an applied research program,

sponsored by the U. S. Department of Housing and Urban Development (HUD), to develop

improved structural test methods for evaluating the performance of housing components.

As an initial step in the program, a comprehensive survey of the literature relating to structural test methods used in evaluating walls, floors, roofs and complete buildings

was conducted. A written survey was conducted among the membership of Committee E-6 , On

Performance of Building Constructions , American Society for Testing and Materials

(ASTM) to help in identifying test method areas in need of basic research. A state-ofthe-art report. Building Science Series (BSS) 58 [1]—^, was published as a result of

the literature survey and written questionnaire. The information obtained from this

initial effort provided the basis for several specific recommendations on fundamental

studies needed to develop improved standard test methods. One of the recommendations

focused on the need for a combined laboratory and analytical investigation of the

section of the existing ASTM Standard Method E72 that pertains' to bearing wall prototypes

tested by in-plane compressive loading.

Numbers in brackets refer to literature references listed in Section 8 of this report.

1
Much of the research that served as the basis for ASTM E72 was conducted at the

National Bureau of Standards (NBS) in the early 1930's. In light of the fact that one

of its primary functions is the development and improvement of methods of testing

materials and structures, NBS was sponsored to study the principal features of several

test methods with the objective of recommending structual test methods applicable to both traditional and innovative building materials and concepts.

As an aid to establishing the investigation plan, contact was made with the members

of the ASTM Committee E6 Task Group that is concerned with the testing of vertical

structures and with several members of the NBS staff who have had experience in testing

innovative wall panels during HUD's Operation BREAKTHROUGH. With the help of written

replies from and direct conversations with several of these individuals, it was possible

to identify several test factors which were of common concern. A summary of the opinions

expressed on the subject of wall compression testing is as follows:

(1) The ASTM E72 Test Method doesn't consider what is often the weakest link -

the details at the top and bottom.

(2) The use of an eccentric loading at the top of the wall while using a flat

bottom condition introduces an unknown eccentricity.

(3) The measurement of end crushing is necessary only if concentric loading is applied.

(4) The specific reference to a fine wire and a mirror for measuring lateral deflection

should be expanded to incorporate modern methods of measurements. More desirably,

a general description of the gage lengths and graduations of the measuring

instruments should be included.

(5) Lateral deflections should be made at the level of maximum deflection, which

may not always be at midheight

.

(6) The selection of a specific eccentricity for standardization is arbitrary.

An improvement to the standard could be made by removing the reference to

a specific eccentricity and writing the standard method in a general manner

that permits the selection of a specific eccentricity dependent on the nature

and type system to be tested.

(7) In positioning the instruments for measuring either axial or lateral deformation,

consideration must be given to the geometry and composition of the specimen as well as to the method of attachment of the instruments to the specimen.

1.2 Obj ective-The objective of this investigation was to develop an improved method of

testing bearing wall prototypes under in-plane compressive loading. As it was intended

that the improved compression test method would be recommended for adoption as a national

voluntary standard, two limitations were placed on the investigation: (1) the recommended

test method must be generally applicable both to traditional and innovative concepts in

wall construction, and (2) the recommended test method must be simple enough in detail

to be practicable for the majority of testing facilities. The objective was approached

by first identifying the principal test factors and then studying them experimentally

or analytically. --
1.3 Scope - Five types of wall panels were selected as being a representative sample

of both traditional (e.g., wood-frame) and innovative wall constructions. The sample

walls, consisting of 4-ft wide by 8-ft high (1.2-m by 2.4-m) specimens, were constructed

as follows:

(1) light-gage steel framing faced with single layers of gypsum wallboard and

insulating fiberboard,

(2) wood framing faced with single layers of gypsum wallboard and plywood,

(3) sandwich panels consisting of a paper honeycomb core and woven roving fiberglass

laminate skins; the panels were faced with single layers of gypsum wallboard,

(4) sandwich panels consisting of a corrugated fiber glass-reinforced polyester

laminate core and skins made of the same material as the core, and

(5) sandwich panels consisting of a f oamed-in-place urethane core and skins of

single layers of asbestos cement and plywood.

The use of masonry wall sections was considered, but the literature revealed that

considerable research has been devoted to investigating procedures for testing masonry

walls with in-plane compressive loads.

A total of 25 compression tests was conducted in the laboratory, using the specimens

whose constructions were described above. For a more detailed description of the test specimens and the prevailing conditions for each test, refer to table 1 in section 2.1.

In each experiment, the load was applied by hydraulic rams and the corresponding deformations were measured with electromechanical gages. For monitoring the deformation

response of the specimens, visual observation and still photography were used.

The test factors considered in this investigation are listed below along with a description of the scope of the investigation relative to each factor.

(1) eccentricity of loading - An end loading fixture was designed to permit the

application of load at several eccentricities. Two eccentricities of loading were used in the laboratory investigation to assess the feasibility of using the

fixture and to observe the effect of different eccentricities on the behavior of

the wall panels

.

(2) load distribution - An analytical study was conducted to investigate the problem

of selecting load distribution hardware that is stiff enough to effect a uniform

distribution along the top of a test specimen. An algorithm was derived, based

on the theory of beams on elastic foundations, for determining the degree of

load uniformity after selection of a load distribution assembly and the number

of discrete loading points. A computer program was written in Fortran language,

based on the derived algorithm. The results enable the user to simply calculate

the maximum allowable axial stiffness of wall specimens for various combinations

of number of loading points and distribution assembly stiffnesses to ensure approximate uniform loading, within an acceptable tolerance.

3
(3) end conditions - Two idealized end conditions were used in the testing program:

(a) pinned at the top and pinned at the bottom and (b) pinned at the top and

• flat at the bottom. Also, the amount of end restraint against lateral movement

of the specimens was varied through the use of end fixtures with adjustable

angles. End restraint variations were introduced to determine the effect, if

any, of the variations on the load capacity and mode of failure of identically

constructed walls.

(4) monitoring and measuring deformation - In each test electromechanical gages were

placed to measure deformation as outlined in the Standard ASTM E72-74. Visible

signs of structural distress and the mode and location of failure were noted and

related to the established gage locations.

(5) significance of results and number of specimens - A study of statistical parameters

was conducted with the objective of determining what parameters would most effectively describe the significance of test results generated by testing wall prototype

After establishing the desired statistical parameter, the study was concluded

with a recommendation for the minimum number of specimens needed to make reliable

predictions.

1.4 History - On August 6, 1937, the National Bureau of Standards published a letter

circular (LC-502A) [2], in which were described test procedures to be used in determining

the structural strength and stiffness of walls, partitions, floors and roofs. The

stated intention was to develop standardized test procedures that would provide a reasonable basis for evaluating the merits of new construction. The circular established

the number and size of specimens, the test conditions and the measurements to be recorded

for a series of structural tests. In the compression test procedure, triplicate specimens,

4-ft wide X 8-ft high, (1.2-m by 2.4-m) were to be tested as columns having a flat-end

bottom support, with load applied to a steel plate covering the top of the specimens.

The load was to be applied uniformly along a line parallel to the inside face and onethird the thickness of the wall from the inside face. The loading was to be applied in

equal increments until maximum load was reached; at each increment of load a reading of

axial shortening was to be recorded. After recording the shortening, the load was to be removed and the unrecovered deformation or set to be recorded. Because the letter

circular was prepared as a result of a research program focused on low-cost construction,

it established minimum requirements for what appeared to be the most important structural

properties. These minimum requirements provided performance limits for deciding if a construction prototype warranted further study.

On August 10, 1938, NBS published the first formal report that described methods used

in the NBS structures laboratory for measuring the strength, stiffness and resistance

to local damage of various types of building construction. The publication. Building

Materials and Structures (BMS) 2 [3] , contained details of the measuring apparatus and

recommendations for reporting test results. It also cited the requirements for loading.
size and number of specimens. In reference to the recommended height (8 ft) of specimens

for compression testing, an explanation was offered as to how that dimension was established:

"A height of 8 feet from floor to ceiling has been widely recognized as satisfactory

for a low-cost house. Therefore, a height of 8 feet was selected for the wall specimens

for compressive load. This is about the least height that can be used in a low-cost

house. The actual height of a wall may be somewhat greater than 8 feet depending

upon connections between wall and floor, roof, etc. For a wall, as for any column,

the higher the wall, the lower the compressive strength. Most walls for low-cost

houses are short sturdy columns; therefore, the strength is about the same for any

height used in a house. For some constructions, particularly thin walls, the strength

may be much less if the height is greater than 8 feet; it may be necessary to determine

the relation between height and strength of these constructions by making additional

tests. It appears probable that the strength of a wall, having a height greater than

8 feet can be estimated by the usual engineering methods with sufficient accuracy for

practical purposes."

The limiting of the floor-to-ceiling height to 8 feet appears to be applicable to houses in general, irrespective of cost. It is not clear whether the authors of BMS 2 were actually referring to "small houses" in the statement about height limitations, as opposed to "low-cost houses".

The description of the loading included in BMS 2 is identical to that presented in

Letter Circular LC-502A. No rationale is offered in either publication for the selection

of the designated end conditions. Also, there is no explanation given for stipulating

the eccentricity as one-third of the wall's thickness measured from the inside face.

Apparently, the required eccentricity reflected a conclusion to apply the compressive

load at the outer limit of the theoretical "kern area" described in theoretical texts

on column behavior. The kern area is defined as that portion of the cross section

within which an axial force can be applied without causing a stress of opposite sign at any point. At this point in the development of the compression test method, there were

no recommendations for rate of loading and hold, or waiting, time at a given level of

loading

.

The compression test method incorporated the measurement of two modes of

deformation: 1) shortening of the specimen and 2) lateral deflection at mid-height. In order to measure the shortening at various load increments, four compressometers were

specified, two on each of the opposite faces of the specimen. As described in the

report, a compressometer consisted of a metal rod, two brackets and a dial micrometer.

The metal rod was supported near the top of the specimen by a bracket and at its lower

end it was seated in a hole in the spindle of the micrometer. The micrometer was supported,

with the spindle up, by the other bracket. The dial was graduated to 0.001 in (0.025 mm).

In order to measure the lateral deflections two def lactometers were used. T'-

5
each edge of the specimen was attached a def lectometer , which consisted of a small

diameter wire, two clamps, rubber bands and a mirror. Half of the mirror was covered by

a graduated paper scale. The wire was attached at its upper end to one of the clamps

and at its lower end to the rubber bands. The rubber bands were stretched to make the

wire taut and were connected to a clamp located near the bottom of the specimen. The

mirror xjas mounted horizontally to the edge of the specimen at midheight. The scale was graduated to 0.1 inch (2.54 mm). As the wall deflected laterally, the image o-f the

wire, reflected on the mirror, marked the point to be read and recorded.

The test results were to be reported in tabular form_. The deformations recorded

by each def lectometer and each compressometer at the various load increments were to be

reported along with the set observed after removal of each load increment. The maximum

load for each specimen was also included as necessary information. Even though axial

shortening and lateral deflection were measured in this method, the method was applied

essentially as a strength test. As there had not been established the degree of

correlation between the test-induced deformations and corresponding behavior in actual

structures, the test results had minimal value as a measure of stiffness. The test

results so obtained by this method were beneficial, however, in establishing the relative

performance of different types of construction when subjected to an identical set of

loading and boundary conditions.

On May 7, 1947, a set of test methods for evaluating the structural properties of

building components was accepted by the American Society for Testing Materials (ASTM)

with a "tentative" status. These tentative methods, ASTM E72-47T [4], were virtually

identical in content and presentation to the recommended test methods cited in BMS 2. In the section pertaining to the reporting of test results, ASTM E72 went a step further

than BMS 2 by requiring a graphical presentation of load, lateral deflection, shortening

and set data. The section in ASTM E72 which related to the size of the specimens

contained a note of explanation for the selection of the 8-ft (2.4-m) height with one notable word change from the paragraph included in LC-502A. The reference to a satisfactory

floor-to-ceiling height for "low-cost houses" was replaced by a reference to "small

houses"

.

In 1954, ASTM Method E72 was adopted as a standard entitled. Standard Methods of

Conducting Strength Tests of Panels for Building Construction . The standard underwent

some revision in 1955; however ASTM E72-55 did not present any changes in the sections

relating to in-plane compression testing of wall panels.

In 1961, ASTM E72-55 was revised as a standard and was given a new designation,

ASTM E72-61 [6], reflecting the year of latest adoption. ASTM E72-61 [7] underwent

extensive editorial changes in June 1965; the major changes affecting the sections on compression testing of wall panels are as follows:

Test Specimens - Instead of designating the specimen height to be 8 feet (2.4 m)

,

the revised edition specified that each specimen was to have a height equal

to the height of the element.

6
Apparatus - The figures illustrating the apparatus were improved by replacing the

original schematic drawing and photographic view with two detailed schematic

views of the specimen as equipped with the compressometers and def lectometers

.

Loading - For the first time the schematic diagram depicting the manner of loading

included an illustration of a steel wide-flange load distribution beam

located atop a steel plate which covered the upper end of the specimen.

Also, the adopted rate of loading (corresponding to a movement of the testing

machine crosshead of 0.03 in/min (0.013 mm/sec) for wood construction was specifically cited in the loading paragraph. No explanation is given for

the selection of this particular rate of loading except to say that it has

been found to be satisfactory. Furthermore, no reason was given for the

fact that no recommendations were made as to the loading rate for other

types of construction.

The latest edition of the ASTM Standard, E72-74 [8] was approved September 19,

1974. The sections related to compression loading on walls remained unchanged from the

corresponding sections in the revised version of E72-61 [7].

7
2. LABORATORY EXPERIMENTS

Compressive load tests were performed on specimens of traditional wood-frame wall

construction as well as on specimens representing proprietary wall panel systems.

Testing was conducted as a means of studying procedures in an effort to develop an improved test method for recommended use. Therefore, the numerical results were end

products gained from exploring various techniques and are not to be considered as evaluations of the specimens for reference. A summary of the tests performed is given

in table 1. - ^ , ; ...^ . . »

2.1 Description of Specimens

2.1.1 Wood-frame Construction - The wood-frame wall specimens were 4 ft by 8 ft (1.2 m

by 2.4 m) and were constructed with a single bottom plate and a double top plate (figure

2.1). Studs were spaced nominally at 16 in (0.4 m) on centers; some specimens contained

3 studs (designated WFTH) and others contained 4 studs (WFFR) placed as shown in figure

2.1. Studs and plates were nominal 2 by 4 members of Construction grade Hem-fir and were fastened with 16-penny (16d) common nails. Single sheets of 4 ft by 8 ft (1.2m

by 2.4 m) gypsum board, 1/2 in (12.7 mm) thick, and 24/0 CD grade plywood, 3/8 in (9.64

mm) thick, were used as interior facing and exterior sheathing, respectively. These

sheets were fastened to the framework with 6d common nails spaced 6 in (0.152 m) centerto-center along the plates and at 12 in (0.305 m) center-to-center along the studs.

Facing edges of the 3-stud panels (WFTH) were braced by wood spacers as shown in fig.

2.1. The overall thickness of the specimens was 4 3/8 in (0.111 m)

.

2.1.2 Steel-frame Construction - These panels (designated STLS) were nominally 4 ft by

8 ft and contained a frame fabricated of galvanized light-gage steel members which had

a 0.05-in (1.3-mm) thick "Z" cross section (figure 2.2). The frame contained three

studs, one at the middle of the 4-ft width and one at each of the two vertical 8-ft

edges of the panel. The same "Z" sections were used to form the two horizontal members,

one at the top edge and one at the bottom edge. The "Z" section members had a 3 5/8-in

(92.1-mm) web, one flange 1 1/2 in (38.1 mm) wide and the other 1 1/8 in (28.6 mm)

wide. Pointed barbs, which were 3/8 in (9.6 mm) wide and 1 in (25.4 mm) long, were punch-formed along the length of the 11/2 -in(38.1-mm) wide flange. The web at both

ends of the horizontal members protruded beyond the flanges, was bent 90° over the ends

of the stud webs and was fastened to them with one sheet metal screw at each connection.

Both of the flanges of all three studs protruded at both ends (as tabs) and were drilled

for single-nail-fastening to the top and bottom wood plates (nominal 2 by 4) that were

added later as part of the wall panel assembly. The flanges of the top and bottom

horizontal "Z" section members were notched out where needed to allow the extended stud

flange tabs to pass through. There was no fastening of the center stud to either top

or bottom horizontal "Z" member. The steel members of the frame were so oriented that

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all barbs were on the same side of the frame. The barbs were used to fasten, by piercing

and clinching, a 4-ft by 8-ft (1.2-m by 2.4-m) sheet of 1/2-in (12.7-mm) asphaltimpregnated insulating fiber board to one side of the frame as the exterior sheathing

of the wall panel. The opposite, or interior, surface of the panel was a 1/2-in (12.7-

mm) thick, 4-ft X 8-ft (1.2-m by 2.4-m) sheet of gypsum board. This was fastened to the steel frame by one plastic rivet at each of the 4 corners and by adhesive applied

to the flanges of all frame members. The wall panel cavity was filled with glass wool

insulation

.

2.1.3 Fiber glass-reinforced polyester panels - Wall panels which were fabricated of

sheets of polyester reinforced with chopped glass fibers were designated (GFRP) . As shown in figure 2.3, the basic panel, nominally 4 ft x 8 ft by 3 5/8 in, (1.2 m x 2.4 m

X 92.1 mm) consisted of a facing, approximately 0.08 in (2.0 mm) thick, bonded to each

side of a corrugated core, made of a similar sheet 0.05 in (1.3 mm) thick, with a polyester adhesive. All four edges of the panel were closed off by U-shaped sections

(similar to the corrugation material) adhesive-bonded to the faces in a re-entrant

position. The exterior surface of the panel was sprayed with a polymer-aggregate

coating for architectural effect. Rock v^ool insulation filled the vertically oriented

voids formed by the corrugated cores. In preparation for testing, top and bottom wood

plates (nominal 2x4) were epoxy-bonded within the existing top and bottom edge Usections to simulate field attachments of bearing members.

2.1.4 Foamed plastic core sandwich panels - These test specimens which were nominally

4 ftx8 ftx 3 in (1.2mx 2.4mx 76.2 mm) were marked (ACUP) . Their exterior face was a 1/8-in (3.2-mm) thick asbestos cement board covered with an epoxy adhesive and

decorative stone. The core was filled with f oamed-in-place polyurethane of 2 pcf (3.2

3 kg/m ) density and the interior facing was a sheet of 1/4-in (6.35-mm) thick pl%nv'ood

.

All of these components were contained by an aluminum-extrusion frame shorn in figure

2.4. The section of the frame was shaped for splining to matching extrusions, for the

attachment of panels to adjacent panels, roof and floor.

2.1.5 Paper honeycomb sandwich panels - Specimens which were designated (GPHC) , contained

composite facings of gypsum board and fiber glass woven roving cloth bonded with polyester

resin to both sides of a paper honeycomb core. Figure 2.5 shows an exploded view of

the basic sandwich panel composition used in the wall construction specimens tested.

The glass fiber reinforced plastic laminates formed the structural (load resisting)

component of the composite facings. The wall specimens were nominally 4 ft x 8 ft x 4 3/8 in (1.2 m x 2.4 m x 0.111 m) . The upper and lower 3 in(76.2 mm) of the core (top

and bottom plates) in each panel, consisted of laminated plwood bearing blocks bonded

to the fiber glass cloth and the honeycomb core. The design of the wall panels requirp"

the application of compressive loads to the walls through the wood bearing blocks

11
without any load bearing on the gypsum board facings.

2.2 Loading Procedures

2.2.1 Test Load Reaction Frame - Compression tests were performed within an adjustable

steel frame (figure 2.6) composed of bolt-connected beam and column sections. The

frame was bolted to a structural test laboratory tie-down floor. It should be noted

that the same purpose can be accomplished by using a self-contained, closed, 4-sided

frame of sufficient strength and rigidity without need for a tie-down floor.

2.2.2 Loading Fixtures - Compressive test loads were applied to the top end of all the

walls by the knife-edge fulcrum fixture shown in figure 2.7. The fixture was designed

to make possible the application of line loads having various eccentricities on test walls of different thicknesses. Instead of making the fixtures continuously adjustable

to produce eccentricities (relative to the centerline of the specimen) ranging from

zero to one-half the wall thickness (i . e . , 0-»t/2) , the bearing plates were notched to provide for three specific eccentricities, of 0, t/6 and t/2 on a centrally placed

specimen of 4-in (0.10-m) thickness. The lateral adjustability of the slotted, containingangles provided for modifying the three specific eccentricities, in addition to accommodating

specimens greater than and less than 4 in (0.10 m) in thickness. At the bottom end of

the wall specimens, two alternative support conditions were used: (1) pin-end and (2)

flat-end. Where a pin-end bottom was called for the specimen was supported on a fulcrum

assembly identical but inverted, to the one used at the top end (figure 2.8). For the

flat-end-bottom condition the bottom fixture consisted of a flat steel bearing plate.

The specimen rested on the bottom fixture. Above the top knife-edge base plate, at each of four points of load application located along the specimen width, there were

arranged in tandem, a load cell and a hydraulic ram. The interconnection of these

elements is shown in the photograph of figure 2.9. The 30-ton (267-kN) capacity, rams were rigidly mounted on the box beam of the reaction frame and were hydraulically

operated from a single manifold by a flow-controllable motorized pump. A. schematic

diagram of the hydraulic loading system is shown in figure 2.10. An analytical method

for determining the number of discrete load points needed to achieve a satisfactory

distribution of load and the theory behind the m.ethod are discussed in section 3.1.

2.2.3 Rate of Loading - Since, in undertaking these tests, rate of loading was a subject open for discussion, no firmly established rate was adopted. Such a selection

is largely influenced by the strength and stiffness of the specimen and the need to obtain accurate data at enough load levels to determine a meaningful load-deformation

performance curve. In choosing a loading rate, it is necessary for the rate to be slow

enough so that the rate of accompanying deformation does not lag behind the test load

development, but extremely slow rates must be avoided in order to conduct a test in a reasonably short time. After some preliminary consideration of previous testing experience

12
and of anticipated maximum loads, it was decided that for the purpose of these experiments

a suitable loading rate would be one which permitted a test to be completed in approximately

one hour (with modification as needed). For the width of specimens, 4 ft (1.2 m) , and

number of rams involved (4), this resulted in a basic rate of approximately 80 lb/ft -min

(19.5 N/m«sec) and was altered for some circumstances (e.g., during accelerated deformation

accompanying incipient failure) . It was noted that at this approximate rate of load

application, an X-Y recorder used for plotting the deflection as a function of load,

did not indicate any deformation lag at the incremental measurement stops; and that,

for monitoring load application by a load cell connected to a digital voltmeter, the

rate of digit change which confronted the pump operator was equal to one digit (i.e.,

0.01 mV or 14 lb/ram) every 10 seconds, a rate not difficult to regulate.

2.3 Instrumentation and Measurements

2.3.1 Load - At each location of load application (i.e., at each ram) the measurement

of forces was made by means of an electrical resistance type load cell of hollow-steelcylinder design. Each load cell had a calibrated capacity of 25 kips (111.2 kN)

.

Loads were applied through these load cells and measured in increments of 250 or 500 lb

(1.11 or 2.22 kN) per ram, depending on the anticipated strength and stiffness of the

specimen. The electrical signals from all of the load cells, as well as other transducers

described below, were fed into the data logging equipment described below. The signal

from one representative load cell was also simultaneously fed to a digital voltmeter

and to the vertical axis of an X-Y recorder for monitoring of the test progress by

equipment operators and observers.

2.3.2 Deformation - Deformations or displacements of the specimens were measured by

linear variable differential transformers (LVDT'S). These transducers measured flexural

transverse deflection and longitudinal shortening of the wall panels subjected to vertical compressive loads. The LVDT's were of three different calibrated ranges (+ 3 in, + 1 in, + O'l i'^) depending on the anticipated displacement to be measured; all

transducers had a total range output signal of about + ^-5 volts.

In order to measure vertical shortening of a wall, compressometers were made by

mounting an LVDT in one end of an aluminum tube to achieve long gage lengths. As shown

in figure 2.11, the empty end of the tube was pin-connected to the panel at its top.

At the bottom end, the sliding core of the LVDT contacted a reference bracket that was attached to the wall. Also, close to the bottom end, the tube was connected by rubber

bands to a V-notched guide bracket that was attached to the wall. The bracket guided

the sliding of the tube as the wall shortened under load.

Lateral deflection of the panel was measured by LVDT's which were mounted transversely

on similarly constructed aluminum tube supports (figure 2.11). The LVDT's were oriented

in a direction parallel to the expected deflection and were attached to the tubes at the several levels at which deflection measurements were desired. It should be noted

13
that in attaching the lube susp* asion pins to the wall, regardless of whether a face or

an edge surface is involved, the orientation of the axes of the pins in the horizontal

plane must be parallel to the neutral surface of the wall in order to permit unrestrained

pivoting of the tubes as the wall ends are rotating. All of the LVDT output signals were fed to the data logging system. In addition, one LVDT which detected mid-height

deflection of the wail was simul »- ^neousl / connected to the horizontal axis of the

monitoi Ing a-Y recorder. , -

2.3.3 Recording - All load ceils and displacement transducers were calibrated, using NBS

traceable standards, before use in the tests. Load cell readouts were accurate to at least within + 1% and LVDT readouts were accurate to within + 0.5%. The data for all

tests were acquired by use of a computer-controlled automatic scanning data acquisition

system which had a capacity of 200 signal channels. The voltage signals from all load

cells and LVDT's were recorded on magnetic tape by the data logging system at each load

increment and as digital printout by a teletypewriter upon demand. The data recorded on magnetic tape were subsequently processed by an electronic computer which converted them to engineering units printed out in tabular and graphic forms.

14
16'

3/8" C D PLYWOOD ^

4«"x96"

2x4 CONSTR. GRADE

\| HEM-FIR STUD (TYP.)

SECTION A-A

7

~"

^ Vi" GYPSUM W.B.

48"x96'

DOUBLE 2x4 TOP PLATES

CONSTR. GR. HEM-FIR

A

6d COMMON NAIL

6" O.C. (TOP & BOn.

6d COMMON NAIL @ 12 " O.C. (TYP.) TP

PARTIAL ELEVATION - 4 STUD ASSEMBLY (WFFR)

16" 16" 8'

PARTIAL ELEVATION - 3 STUD ASSEMBLY (WFTH)

Figure 2.1 - Wood-frame construction test panels (OTFR, OTTH)

15
FOLDED. J WEB

I

I I M I 1

I I

18 GAGE GALVANIZED

STEEL STUDS '

'7

V/2- I

-I ^ ADHESIVE

I I 2" INSULATION 7 ^ *10x/2" SHEET

"I METAL SCREWS

.1/2" FIBERBOARD

I

I

I

I II M Ml II II I I^C I I M I

I I

1 5/16" _ i POINTED BARB 22 21/32'

]_l_l_l_i_L_l_i_l_

J I M M I I I

I I 1 M I M

if

22 21/32'

I M M I 1 II

|-

1 5/16"

48"

HORIZONTAL SECTION THRU PANEL

o

o

PARTIAL EXTERIOR ELEVATION

* STEEL PANEL FRAME

w/o FACINGS

Figure 2.2 - Steel-frame construction test panel (STLS)

.

16
4'-0"

CROSS SECTKDN U-SHAPED SIDE

CLOSURE (TYP.)

2x4 WOOD PLATE OTYP.

1^

U-SHAPED

END CLOSURE (TYP.

SDE VIEW

Figure 2.3 - Glass-fiber reinforced plastic test panel (GFRP)

17
Va" plywood

1/8" ASBESTOS CEMENT

BOARD

POLYURETHANE FOAM

DECORATIVE GRAVEL IN

EPOXY MATRIX

ALUMINUM EXTRUSION

Figure 2.4 - Foamed plastic core sandwich test panel (ACUP)

.

18
STRUCTURAL SKhi :

SURFACE: 5/8"TYPE x' GYPSUM WALLBOARD

HONEYCOMB

Figure 2.5 - Construction of paper honevcomb sandvich test panel (GPHC)

.

19
Figure 2.6 - Typical compression test setups.

20
Figure 2.7 - Fulcrum loading fixture for pin-end condition.

21
Figure 2.8 - Profile of typical pin-pin loading setup.
i

Figure 2.9 - Interconnection of upper test-apparatus elements.

COARSE FLOW

CONTROL VALVE

ii^ ADJUSTABLE

I CONTROL VALVE

I

VARIABLE SPEED

ELECTRIC PUMP

BY-PASS

CHECK VALVE

J- J

/30-TON

HYDRAULIC RAM

Figure 2.10 - Schematic of hydraulic loading systt

23
gure 2.11 - Mounting details of LVDT's,

24
3. ANALYTICAL m'ESTIGATIONS

3.1 Load Distribution - A very i-porcant practical consideration in the development of

a test method for evaluating the conpressive resistance of walls is the procedure for

applying the load to the specimens. The usual practice is to use several hydraulic

rams to apply concentrated loads to a distribution beam which in cum distributes the

total load to the top of the wall specimen. The technical problem lies in the determination

of the design of the load distribution assembly so as to effect a good approximation of

uniform loading. The variables under the control of the evaluator are the number and

position of the loading rans and the stiffness (EI) of the distribution beam. The

greater the number of rams and the stirrer the distribution beam - relative to the

axial stiffness of the wall specimen - the closer one comes to achieving uniform

loading. This fact not withstanding, the economics of conducting performance tests

dictate that one attempt to optimize the distribution system. The problem then, is to derive a method for designing the load distribution system that leaves the decisions as

to the maximum tolerable deviation from uniformity and the allocation of equipment to the evaluator.

The conditions of this technical problem were found to have a theoretical analogy

in the theory of elastically supported beams. In defining the conditions of support,

Hetenyi [10] states that "elastic support is provided here by a load-bearing medium,

referred to as the 'foundation,' distributed uniformly along the length of the beams."

The fundamental assumption in this theory is that the magnitude of resistance provided

by the foundation at any point is proportional to the vertical deflection, y, of the

beam at that point. Assuming the supporting material obeys Hcoke's lav, its distributed

reaction, p, can be expressed as follo-^-s:

p = ky

where k is called the modulus of the foundation or foundation constant, expressed in

units of Ibf per inch of wall per inch of deflection (newton per meter per meter) . The

deflection curve of the bear: can be expressed in terms of a fourth-order differential

equation:

Eld

dx

4

= -^y ^ q

where q represents the intensity of distributed loading on the beam. Tae particular

case in the theory which relates to the problem is that of beams of finite length with

free ends. Taking the associated boundary conditions into account, Hetenyi has provided

solutions for various selected loading cases. To obtain a solution for a number of

concentrated loads, spaced equally along the length of the beam, it is only necessary

25
to apply the fundamental principle of superposition. Thus, the basic equations are available to enable the computation of the deflection - and, hence, the intensity of

foundation reaction - at any point along the beam, for a combination of loadings.

On the basis of the above mentioned analytical tools, an algorithm was developed

to optimize the selection of the load distribution assembly. The initial step of the

method is to compute the magnitude of the foundation (i.e., wall) reaction, as a function

of the deflection and an initial trial foundation constant - at several key locations

along the distribution beam. These discrete values of foundation reaction are then

averaged and their respective deviations from the average are computed. This procedure

requires the input of several variables: (1) EI of the beam assembly, (2) the number

and location of the concentrated loads and (3) the absolute value of maximum variation

from uniform load distribution that will be allowed. The output from this procedure is

a value of the maximum stiffness of wall specimen that can be tested for the selected

EI and load input without exceeding the maximum allowable load variation specified.

The process for obtaining the desired output is an iterative one and a computer program

was written to facilitate the tedious computations. The details of the computer program

are discussed in Appendix A. A practical application of the analysis is illustrated in

the proposed standard test method which is presented in section 6. Approximate foundation

constant values were computed for some typical wall constructions and they are presented

in tabular form (table 6.A.1) in the same section.

3.2 Eccentricity of Loading - Because Che horizontal components (such as floors, roofs

ceilings) of buildings connect to exterior walls unsymmetrically it is customary to think of testing bearing wall prototypes by applying an eccentric axial, compressive

load. In fact, ASTM Standard E72 has standardized the eccentricity by specifying that

it shall be applied along a line located one-third the thickness of the specimen from

the surface of the inner facing material. The rationale for this specific eccentricity

requirement was not determined during this study, but the one-third fraction brings to mind the postulate of a core or kern radius. The core is defined by Shanley [9] (e.g.)

as "that portion of the cross section within which an axial force can be applied without

causing a stress of opposite sign at any point."

CORE OR KERN

b

Figure 3.1 - Kern geometr> of a rectangular cross section.

26
There is implicit value in knowing the boundaries of this area in types of construction

in which tensile stresses are to be avoided. Figure 3.1 illustrates the concept of the core and core radius for a homogeneous material of rectangular cross section.

In figure 3.1 the symbols are as follows:

P - axial load

a - extreme fiber stress

h - height of cross section

b - width of cross section

- distance parallel to the y-axis from the edge to the centroid of the area

C - distance parallel to the xaxis from the edge to the centroid of the area

X , x,y - principal axes

r - core radius

c N.A. - neutral axis or axis of zero stress for pure elastic bending

The concept of the core as pictured above is not generally applicable to walls

because the majority of wall types are heterogeneous. Most types of wall construction

consist of at least two different materials that are joined together to form a structural

unit. The kern radius of composite walls can be located if their cross sections are "transformed" into an equivalent cross section of uniform properties. One of the materials

is taken as a base and then the other materials are transformed, in proportion to the

ratio of their respective moduli of elasticity, relative to that of the base material.

In Appendix B a procedure is illustrated for calculating the cross-sectional properties

of a transformed area. The procedure includes a step for calculating the core radius.

Once the value of the core radius is determined, it can then be compared to the eccentricity

described in ASTM E72. Examples are included to illustrate the use of the procedure for

three commonly used wall constructions. The purpose of performing the calculations was

to establish if the basis for stating the single value of eccentricity, e , was

the concept of kern radius. The conclusion drawn from this exercise is presented in

section 5 of this report.

3.3 Statistical Parameters Needed to Describe Results - The type of calculations required

to report the test results and the kind of predictions that are expected is dependent

upon the type of test that is conducted. On the subject of types of tests, Dorey and

Schriever [11] have distinguished between the objectives of an Acceptance (or Proof)

Test and those of a Rating Test. The Acceptance Test is conducted to evaluate the structural properties of the unit

under test. Simulation of actual boundary conditions is very important in this case. On the other hand, a Rating Test is conducted to establish a maximum test load - or some other performance attribute - for a prototype specimen. Specimens are nominally identical

to the structural components which they represent. In order to project the performance

of the actual, built components, consideration must be given to the variability in

strength and stiffness of the samples. In view of the fact that most performance evaluation

testing of bearing wall construction is conducted on prototypes of the actual, built

27
components, it is concluded that the test results should be reported in a format consistent

with the objectives of a Rating Test. In fulfulling these objectives, the question

arises as to which statistical parameters are germane. Before attempting to answer this

question it was necessary to define the kind of prediction that one desires to make

after testing a sample of wall panels in compression. It is premised that the evaluator

would like to use the performance test results to predict, with a reasonably high level

of confidence, that a high proportion of the population of walls represented by the test sample will possess a strength or stiffness in excess of a certain limit. A study of

the application of the statistical parameters commonly used to describe test results

revealed that the use of one-sided statistical tolerance limits was appropriate for this

purpose. It is important to note that the application of one-sided tolerance limits

constitutes a very significant extension of the current general practice of simply

estimating the mean or variance of the population distribution on the basis of testing

three or more specimens. The concept of one-sided tolerance limits can be expressed in

the following formulation: the probability is Y (e.g., 0.95) that at least a certain

proportion, p, (e.g., 0.90) of a population will be greater than the limit x - ks,

where x is the sample estimate of the population mean and s is the positive root of the

sample estimate of the population variance (i.e., the sample estimate of the standard

deviation). The value of the factor, k, can be obtained from a table of factors for

one-sided tolerance limits for a normal distribution function. Table A-7 in reference

[12] presents a listing of k factors for selected sample sizes and values of y and p. The reader is referred to section 6.9.3 for the step-by-step procedure of calculating

the test results as recommended in the proposed standard test method.

7 '>.;. •-fr; '!• 28
4. DISCUSSIONS

The discussions of the individual test runs which follow correlate with the abbreviated

summary of research tests given in table 1.

4.1 Test Run No. 1 (WFR) - This run and the next three (run Nos. 2, 3, 4) were made on

the same specimen for initial exploratory tests in trying out the equipment of the test

setup. The 4-stad wood-frame specimen was of the type shown in figure 2.1 with the

plywood considered as the exterior face and the gypsum board, the interior surface. The

top and bottom ends of the facings were trimmed back 1/4 in (6.3 mm) from the respective

bearing surfaces to prevent direct bearing of the ateel loading plates on the edges of

the facings. Steel angles, used as end fittings for lateral containment of the ends of

the wall, were bolted in position on the steel bearing plates in contact with the wall

but without lateral pressure. The fulcrums and bearing plate notches were positioned to provide a loading eccentricity of t/6 toward the interior (gypsum) face based on the

gross thickness of the wall section. Arrangement of the LVDT's for measuring transverse

deflection (10 positions) and shortening (4 positions) corresponded to the instrumentation

setup shown in figure 4.1. In this test run the wall was loaded in increments of 250 lb/ft (3.6 kN/m) to a maximum of 1600 lb/ft (23.4 kN/m). Load and deformation measurements were logged after

adding each increment of load. From the maximum load level the wall was unloaded continuously

at approximately the loading rate of 80 Ib/ft/min (19.5 N/m/sec) . The taped data were

considered unreliable because of electronics difficulties which were detected during the

test. However, the x-y recorder provided a graph of the test as represented by the

monitored load-cell and midspan-deflection transducers. The graph exhibited much "staircasing" or "stepping" as opposed to being a smooth curve record of a load-deflection

relationship. At the time of testing the phenomenon was considered attributable to erratic specimen behavior but observations in later tests (e.g., c.f. No. 2) indicated

that the staircasing might be corrected by improvements in LVDT mounting.

4.2 Test Run No. 2 (WFFR) - The setup and procedure for this test were the same as run

No. 1 except that loading was carried to a maximum of 2250 lb/ ft (32.8 kN/m). The

electronics circuitry had been modified but the data output was still suspect. Staircasing

of the x-y record was again evident. However, observation during the test seemed to indicate that the fault was in the manner of mounting the LVDT's used for measuring

transverse deflection of the wall. As shown in figure 4.2 (a), the bullet-nose end of

the LVDT core extension had been glued (hot-melt) to the wall surface reference plate.

While this arrangement provided stability for the LVDT, it did not allow for vertical

movement of the LVDT relative to the reference plate. The relative vertical movement

was caused hy the shortening of the wall which carried the supporting aluminum tube.

The result was a jamming of the core in the coil by frictional force which was overcome

29
intermittently (thus producing a "staircase" graph) during horizontal movement of the core produced by deflection of the wall. It was decided to provide the necessary stability

for the core by replacing the gluing procedure with compression-spring loading of the core as shown in figure 4.2 (b) . This permitted vertical sliding of the bullet-nose on

the reference plate.

4.3 Test Run No. 3 (WFFR) - Run No. 3 also used the same specimen, setup and procedure

as Run No. 1, except that the LVDT cores were spring-loaded as described in 4.2. The

first cycle of loading was carried to 3000 lb/ft (43.8 kN/m) and returned to zero. No

staircasing was observed on the x-y graph. The second cycle of loading was taken to 4000 lb/ft (58.4 kN/m) and returned to zero. From about 3500 lb/ft (51.1 kN/m) up, staircasing was apparent. This time, the jamming of the cores occurred because the

deflection LVDT's were mounted in such a direction (i.e., with cores referenced to the

wall surface which become concave) that the core springs were compressed further as deflection increased, The result was an increased pressure of the bullet-nose against

the reference plate, causing difficulty in sliding between the two, and as before,

consequential friction-jamming of the core in the coil. Upon unloading the wall in the

second cycle, the staircasing disappeared at about the same value of deflection of the

wall as that at which it had started. In future tests, the deflection LVDT's were

oriented so that the core end was referenced to the convex face of the wall. In this

way, wall deflection caused extraction of the LVDT core from its coil and the stabilizing

spring (sufficiently compressed) was allowed to relax, yet perform its function.

During the remainder of the second unloading cycle other aberrations appeared on

the x-y graph. Close observation of the test setup and the graph being generated revealed

that these deviations were caused by irregular "unload-recover" behavior due to ram piston friction being developed by the lateral thrust of the flexed wall which was tending to recover. The electronics circuit was still not trouble-free during this test run

.

4.4 Test Run No. 4 (WFFR) - This test setup and specimen were the same as for run No. 1 except that no LVDT's were used and load cells were read only by the teletype; one load

cell was also used to monitor the load using only the vertical axis readouc on the x-y

recorder. The test was intended to provide information on the mode of failure without

risking damage to instruments. The wall was loaded in increments of 250 lb/ft (3.6

kN/m) to a maximum of 7500 lb/ft (109.4 kN/m). Complete failure of the specimen occurred

at maximum load by splitting of an outer stud near a knot (fig. 4.3). This had been

preceded by crushing and rotation of the top 2x4 wood plates caused by eccentric

loading of the wood plates against the stud ends (a relatively concentrated loading

condition) . Also apparent was evidence of nail heads being pulled through the gypsum

board. Cracking of the gypsum board seen in figure 4.3 was considered secondary, following

the stud failure; quadrilling of the gypsum board had been performed to assist detection

30
of surface distortions visually and photographically. Both the plywood and gypsum board

were cracked near the upper steel containing angles. The gypsum board was also crushed

because of rotation of the top wood plates, resulting in closure of the 1/4-in (6.3-mm)

space between the end of the gypsum board and the steel bearing plate. The corresponding

1/4-in (6.3-mm) space on the plywood side had become enlarged. Electronics difficulties

were still present during this test run.

4.5 Test Run No. 5 (WFFR) - The preceding test (run No. 4) was duplicated by this run with the following two exceptions. Instead of trimming the ends of the facings, an aluminum shim plate, 1/4 x 3 1/2 x 48 in (6.3 x 88.9 x 1219.2 mm) was fastened with

screws to the top and the bottom wood plates of the new specimen to provide clearance

from bearing for the facing edges. The loading eccentricity was 1/2 the gross thickness

of the wall so that the load was in line with the exposed surface of the gypsum board.

The wood plates were beginning to show evidence of crushing-rotation when, at 3100 lb/ft

(45.2 kN/m) , the bottom end hardware slipped off the end of the wall and pivoted about

the edge of the aluminum shim plate (figure 4.4) . Considering that the load eccentricity

was large (t/2) and that it extended beyond the edge of the shim, where there was no wall bearing, the result was not unexpected. Nevertheless, the test was instructive

with regard to hardware performance relative to the development of specimen failure.

Data readouts were still questionable in this test because of continued trouble with the

electronics

.

4.6 Test Run No. 6 (WFFR) - Two modifications of the preceding test run (No. 5) provided

the setup for this run. The loading eccentricity, (t/2), was based on stud width, thus

putting the load line at the interface of studs and gypsum board, and the aluminum shim

plates were not attached to wood plates but, rather, tack-glued to the steel bearing

plates. Otherwise, the test proceeded as before, primarily to observe specimen behavior

under load but without LVDT instrumentation. This new wood-frame specimen was loaded to 4800 lb/ft (70.0 kN/m) at which time the excessive crushing-rotation of the wood plates

was considered to have constituted failure (figure 4.5). This was accompanied by cracking

of the gypsum board at the level of the containing steel angles, as well as by its

buckling near the top. The clearance for the gypsum board edges, provided by the aluminum

shim plates, had been closed up by crushing and rotation of the end plates. However,

the end fittings did not break loose from the wall. The circuitry problem continued to exist.

4.7 Test Run No. 7 (WFFR) - For this test a new wood-frame specimen was used. Only 3 LVDT def lectometers were mounted at one edge of the wall (one at mid-height and at the

upper and lower 1/4-points) . Inadvertently, these three spring-loaded LVDT's were again

mounted with reference plates attached to the interior wall surface (concave) , resulting

in staircasing of the x-y recorder plot (c.f., test run No. 3). The upper end of the

31
wall was fitted with the same hardware (angles, plates and fulcrum) used in preceding

tests, but the bottom end was provided with only a flat steel bearing plate; aluminum

shim plates (attached to the steel plates) were used at top and bottom to provide the

facing edges with clearance from bearing. Loading eccentricity was set at t/6, based on gross wall thickness. The wall was loaded to 4000 lb/ft (58.4 kN/m) in 500-lb/ft (7.3-

kN/m) increments and then unloaded. The top of the wall showed evidence (visual and x-y

record) of permanent deformation by crushing and rotation of the wood plates. The wall

was then loaded incrementally to 7200 lb/ft (105.1 kN/m) at which load the test was halted because of excessive top end-rotation (figure 4.6). The opposite ends of the

wall showed great contrast in behavior as influenced by the respective load bearing

conditions.

With the execution of this test the difficulties which had existed in the electronics

circuit were resolved. For test run No. 7, ^nd all following tests, the electronics

instrumentation data were considered reliable,

4.8 Test run No. 8 (WFFR) - In this test a fresh 4-stud wood-frame wall panel was set up with fulcrums, angles and unattached aluminum shim plates at top and bottom. The

loading eccentricity, t/6, was based on the stud depth of 3 1/2 in (88.9 mm). The

specimen was instrumented with 14 LVDT's attached, generally as in test run Nos . 1-3,

for measurement of shortening and deflection. However, the reference plates for the

def lectometers were mounted on the exterior face of the wall (which became convex), and

each of the LVDT bullet ends was held in contact against the reference plate, by a lightly stretched rubber band. The smooth x-y recorder graph which was obtained in this

test proved this core holding technique to be satisfactory. Several rack and pinion

type dial gages were supported at the wall mid-height by a floor stand to obtain comparative

readings of lateral displacement under load. Comparison of the deflection data from the

dial gages with those obtained from the specimen-mounted LVDT's confirmed that the

specimen-mounted def lectometers provided a more reliable and definitive measurement of

the specimen's deflection. The wall panel was held in place before testing with a small

initial load, loaded to 4850 lb/ft (70.8 kN/m) in 500-lb/ft (7 . 3-kN/m.) increments and

then unloaded gradually, stopping at 3 load levels to make measurements. The main

purpose of this test run was to acquire a representive set of data to be processed by a digital computer into engineering values for tabular and graphic printout. In addition

to simple conversions by use of factors, the program also contained subroutines for

obtaining averages of designated transducers and for plotting multiple graphs on one set

of multiply-labeled axes.

4.9 Test run No. 9 (WFFR) - This run was a second test on the specimen used in the

preceding run. It was conducted primarily to observe the performance of a specimen

(with fulcrum loading at both ends) when the containing steel angle was not used at top

or bottom on the interior (concave) side of the wall panel (figure 4.7). Other aspects

32
of the test setup were the same as for run No. 8. In addition, two floor-stand-mounted

displacement dials were used to detect lateral movement of the test frame box beam and

the top loading plate (figure 4.7). The lateral movements of both of these parts were

very small. At the maximum test load of 4700 lb/ft (68.6 kN/m) with accompanying specimen

deflection of 0.91 in (23.1 mm) the test frame box beam had shifted laterally less than

0.004 in (0.1 mm) and the loading plate with fulcrum, less than 0.05 in (1.3 mm). The

accomodation shift of the box beam was obviously insignificant. The load plate shift,

though minimal insofar as causing an inclined (instead of vertical) load is concerned,

does illustrate the desirability of mounting a def lectometer directly on the specimen

rather than on a floorstand to measure net deflection of the specimen.

The removal of the "inner" steel containing angle at top and bottom (figure 4.7) was an improvement on the end loading conditions. The remaining two "outer" angles (one

each at top and bottom) were sufficient for containing the ends of the wall panel up to the maximum test load. The absence of the two angles on the concave side eliminated

cracking of the gypsum board interior face when the wood plates experienced crushingrotation (figure 4.7). The edge cracking at the top of the gypsum board (seen in the same figure) was a consequence of the closure of the 1/4-in (6.3-mm') gap, provided by the

shim plates to avoid edge bearing of the facings when that space was closed by crushingrotation of the wood plates.

4.10 Test run No. 10 (STLS) - This was the first test to make use of a light-gage steel

stud frame wall panel described in section 2.1.2. The instrumentation and loading

procedure were the same as those used for test run No. 1. Hardware at both the top and

bottom included inner and outer containing angles and fulcrum load points. The loading

eccentricity was t/6 based on the 3 5/8-in (92.1-mm) depth of the Z studs (figure 2.2).

There was no need for shim plates tb prevent facing edge bearing as in previous tests

because the same purpose was served by each of the 2 x 4's attached flat against the

webs of the top and bottom horizontal Z plate members, (fig. 4.8). It can be seen in

the same figure that a stud bottom tab was close to bearing (a condition which would

also occur in use); the protruding 1 1/2-in (38.1-mm) flange at the exterior (fiberboard)

side of the bottom horizontal Z member also approached this condition. However, this same condition did not exist at the top since the protruding (interior) flange of the

horizontal Z section is the shorter (1 1/8 in) (28.6 mm) one. Some of the deflection

measurements at the first few increments of applied load indicated negative deformation

of the wall (i.e., deflected toward the eccentric load). Apparently the negative deflection

was the result of a relative movement of the LVDT coil-supporting tube (with respect to the wall-mounted core) caused by loading accomodations of the horizontal 2 x 4's to which the tubes were attached (figure 4.8).

The x-y record showed some load drop-off at incremental, observation stops (but

without increase in deflection) ; this was thought to be due to slip of screw connections

between sheet metal members. At 3000 lb/ ft (43.8 kN/m) there was evidence of crushing

33
of the bottom 2x4 directly under the web-edge of an outer Z stud (i.e., at the folded

end of the web of the horizontal Z member) . This folded end of the web of the horizontal

Z member was also being bent outwardly. In loading from 3500 to 3800 lb/ft, (51.1 to 55.5 kN/m) there was web buckling of the Z studs visible at the top edges of the wall

panel. The corresponding erratic x-y deflection record was an indication of the influence

of local deformation at the ends of the wall on apparent deflection measurements. This was confirmed by the computer load-deflection plot.

4.11 Test run No. 11 (STLS) - A new steel Z stud frame wall panel was used in this run, the procedure for which duplicated the preceding run (No. 10), except for two features:

(a) one def lectometer supporting tube was mounted over a shorter portion of the wall

height; and (b) the upper and lower interior (gypsum board) face containing angles were

removed after applying the first load increment.

In an effort to observe any benefit derived from avoiding the effect of local

deformation (at the ends of the specimen) on the suspension points of the def lectometer

support tube, the ends of one such tube were supported on the Z stud web at 3 1/2 in

(88.9 mm) from each wall end instead of the previous 3/4 in (19.1 mm) (i.e., the midthickness of the horizontal 2 x 4's). ' The specimen was loaded incrementally to a maximum of 2300 lb/ft (33.6 kN/m). At 1750 lb/ft (25.5 kN/m) the ends of the outer Z studs, at all 4 corners of the wall were

crushing the webs of the horizontal Z members into the 2 x 4's on the interior side of

the wall. At 2300 lb/ft (33.6 kN/m) there was general web buckling near the top and

bottom ends of the Z studs. Contrary to the usually expected behavior, the def lectometers

referenced to end points located farther away from the top and bottom 2 x 4's indicated

significantly more transverse deflection (approx. 3 times) than those referenced over

the greater wall height. The most likely explanation for this anomaly is that the latter

def lectometers were influenced by local crushing at the points of suspension. The

remaining outer angles at the ends of the wall provided satisfactory containment of the

specimen throughout the test (see figure 4.9).

4.12 Test run No. 12 (GFRP) - The specimen for this test was a fiberglass-reinforced

plastic panel with bonded 2x4 wood plates at top and bottom as described in section

2.1.3. Before testing, the plastic facings and U-section legs were cut back 1/4 in (6.3

mm) from the bearing surfaces of the top and bottom wood plates to ensure that the

facings were not in direct load bearing (figure 4.10). Fulcrum loading fittings and

containing angles were used at the top and bottom of the panel. A 1/16-in (1.6-mm)

sheet of rubber was inserted between the angle legs and the specimen to provide better

surface contact (especially on the exterior sprayed-aggregate surface) . The loading

eccentricity was set at t/6 (referenced to the full thickness) toward the interior wall

surface. The interior face of the panel was quadrilled to facilitate observation of

dimnling on the surface. Deflection of the specimen was measured by 5 LVDT's located

34,
along each edge at the following elevations: mid-height, quarter-points and 4 in (0.10

m) from each end. The span of the LVDT pivoted supporting tubes was 93 in (2.4 m).

Load was applied in 500-lb/ft (7.3-kN/m) increments to a maximum of 5400 lb/ft (78.8

kN/m) where failure occurred by sudden loss of adhesive bond between the interior facing

and the core corrugations, followed by wall buckling (figure 4.10). Although relatively

large magnitudes of deflection (1.3 in) (33 mm) and end rotation occurred, the endfittings functioned satisfactorily. The fixtures contained the wall ends and the fulcrums

remained in the notches.

4.13 Test Run No. 13 (ACUP) - A foamed urethane core sandwich panel, of the type described

in section 2.1.4, served as the specimen for this test run. Fulcrum plate and angle

fittings were used at both top and bottom of the wall panel specimen. To achieve better

contact surfaces, the aggregate on the exterior surface of the panel was chipped away at the locations of the containing angles (as well as at the locations of the def lectometer

reference plates for better adhesive bonding) and a double thickness of 1/16-ln (1.6-mm)

sheet rubber was used as an interface. Although the wall height was less than the

nominal 8 f t - 94 1/2 in (2.4 m) - the 5 LVDT's at each wall edge were located at the midheight, 2 ft (0.60 m) above and below mid-height, and at 4 in (0.10 m) from the ends;

the length of the def lectometer supporting tubes was 90 in (2.3 m). The loading eccentricity

was t/6 toward the interior wall surface (plywood) and was based on a nominal wall

thickness of 3 in (76.2 mm) — the depth of the surrounding extruded aluminum frame. No compressometers were used.

The specimen was loaded in increments of 500 lb/ft (7.3 kN/m) to a maximum of

11,500 lb/ft (167.8 kN/m) with an accompanying mid-height deflection of more than 1 1/4

in (31.8 mm). At that point a twisting separation of the aluminum frame from the body

of the wall at mid-height was followed by explosive tensile cracking of the wall. The

sudden release of energy caused the failed specimen to spring out from under the loading

apparatus (figure 4.11). The same figure includes a view of the wall after recovery.

It was observed during the test that it is important to accurately orient the

def lectometer LVDT's parallel to the direction of deflection to avoid binding of the cores in the coils when the core ends are held in place against the reference plates by

rubber bands and to avoid an oblique measurement of the deflection.

4.14 Test Run No. 14 (GPHC) - This test run used a paper honeycomb sandwich panel of

the type described in section 2.1.5. However, this particular specimen had a thinner

exterior surface of a proprietary material similar to, but more dense than gymsum board;

the overall thickness of this wall panel was 4 in (0.10 m) . The test setup included

fulcrum load point assemblies, containing angles and 1/4-in (6.3-mm) face-bearing relief

shim plates (the facing boards were virtually flush with the bearing surfaces of the

laminated wood blocks) both at top and bottom of the specimen. The loading eccentricity

was t/6 based on the full 4-in thickness of the panel. Only transverse deflections were

35
measured, with LVDT's located along both panel edges at the mid-height, 1/4-points and 4 in (0.10 m) from top and bottom (figure 4.12). The length of the LVDT support tubes was

92 3/4 in (2.4 m) . Loading of the specimen in 250-lb/ft (3.6-kN/m) increments, with

short stops for measurement scans, provided a relatively trouble-free, smooth x-y loaddeflection record and corresponding digital data. The failure of the panel was sudden

at a load of 6850 lb/ft (99.9 kN/m) by delamination of the gypsum board from the woven

roving and by wall buckling, at a location just above the bottom plywood block, on the

compression side (figure 4.12). The failure permitted abrupt additional rotation of the

bottom fixture with consequent secondary cracking of the panel faces near the vertical

legs of the containing angles.

4.15 Test Run No. 15 (STLS) - Beginning with this test run a group of five tests (Nos

.

15--19) were conducted using specimens of the various proprietary types tested previously

but employing flat bearing conditions at the bottom, without either containing angle.

This bearing condition was described in section 2.2.2. Fulcrum loading, including use

of both containing angles in contact with outer and inner wall surfaces, was used at the

top. All 5 tests made use of only def lectometer-LVDT ' s (no compressometers) located

along both panel edges at mid-height, 2 ft (0.60 m) above and below mid-height, and at small distances (given in each test discussion) from the top and bottom ends.

Run No. 15 (STLS) was made on a panel of steel-frame construction described in

section 2.1.2. The loading eccentricity was t/6 toward the inner (gypsum board) face,

based on the 3 5/8-in (92.1-mm) depth of the Z stud (figure 2.2). The LVDT supporting

poles were pivoted at 3 1/2 in (88.9 mm) from the top of the wall and lested in V-guides at

5 in (0.13 m) from the bottom; tneir 87 1/2-in (2.2-m) span was totally within Lhe upper

and lower wood plates (i.e., on the Z-stud web). The outermost def lectometers were 7 in

(0.18 m) from the bearing ends of the panel. The specimen was loaded in increments of

250 lb/ft (3.6 kN/m) to a maximum of 3150 lb/ft (46.0 kN/m). The maximum lateral displacement reading was a negative value, -0.03 in (-0.76 mm), indicating movement toward the

gypsum board face. This apparent negative translation is opposite to that expected for

the direction of load eccentricity. While it was observed that the studs experienced

very little bowing, it was concluded that the sign reversal was the result of the local

distortion observed at the top of the studs. The localized deformation caused top plate

rotation (fig. 4.13) and probable shifting of the pivots at the end of the LVDT support

poles. This explanation was supported by the erratic nature of the x-y recorder plot

and of the digital data.

4.16 Test Run No. 16 (GPHC) - The specimen for this test was a paper honeycomb sandwich

panel described in section 2.1.5. The loading eccentricity for the pin-flat setup was

set at t/6 - with respect to the full thickness, 4 3/8 in (0.11 m),of the panel - toward the interior face. The pivots for the def lactometer LVDT support poles were

attached 1 1/4 in (31.8 mm) from the top and the V-guides, 2 1/4 in (57.1 mm) from the

36
bottom thus making the poles span from upper to lower wood blocks. The LVDT's which

were farthest from the mid-height, were at 4 in (0.10m) from the top and bottom ends.

Bearing of the gj'psum board facings was prevented by use of 1/4-in shim plates over the

wood block bearing areas. Comparative measurements of lateral displacement of the

middle of the interior face were made with a rack and pinion dial mounted on a floor

stand in 250-lb/ft (3.&-kN,m) load increments up to a maximum of 6900 lb/ft (100.7 kN/m)

;

the maximum deflection was approximatelj' 1/4 in (6.3 mm). Failure occurred at the top wood

block by separation from the facing (figure 4.14). Subsequent rotation of the top end

caused the exterior gypsum board to crack. The displacement dial readings generally agreed

with the average of the mid-height L\T)T's for the first few load increments but for the

rerainder of the rest, they were repeatedly, but not sj'stematically , higher. At several

scannir.g steps the waiting period was deliberately extended to two minutes to obser\'e the

effect on the test setup. Within the range of linear response (i.e., up to 5000 lb/ft)

(73.0 kN/m), load drop-off ranging from 100 to 300 lb/ft (1.5 to 4.4 kN/m) was observed.

This load drop—off was a function of the hydraulic system, and was not accompanied by

creep deflection. Beyond the linear range, load drop-off during extended waiting was accompanied by creep-deflection.

4.17 Test Run No. 17 (GFRP) - This test run was made on a fiber glass-reinforced plastic

panel described in section 2.1.3. The pin top-flat bottom arrangement, which included

bearing shim plates, had a loading eccentricity of t/6 toward the smooth interior face

which was quadrilled for better observation of surface deformations (figure 4.15). The

upper-and lower-most LVDT's were at 4 in (0.10 m) from the ends of the wall; the LVDTsupporting poles extended from 1 in (25.4 mm) below the top to 2 1/2 in (63.5 mm) above

the botton, the wall height being 96 1/2 in (2.5 m) . Loading was in 500-lb/ft (7.3-kN/m)

increments. Figure 4.15 shows the panel during testing at a load of 4900 lb/ft (71.5 kN/m)

after the test when failure had caused the bottom end to suddenly shift laterally'. Failure

occurred by buckling bond-separation of the exterior face from the corrugated core at about

1 ft (0.30 m) up from the bottom. It should be noted that, being a flat-end bearing, the

bottom end was partially restrained from rotation. The bottom portion of the wall where the

failure developed was probably well below the inflection point of a column member under

such loading. The result was that the exterior face was quite apparentlj? under compression.

Buckling in this direction caused the bottom of the wall to suddenly translate in the

direction of the interior surface, carrj'ing with it the bottom shim plate which is seen up-ended in figure 4.15. Shim plates were used with this type specimen, in this test

to avoid cutting back the facings near the bearing ends.

37
4.18 Test Run No 18 (ACUP) - A foamed urethane core sandwich panel was set up as seen

in figure 4.16. A load level of 10,800 lb/ft (157.6 kN/m) was recorded just prior to failure. Based on the experience with a similar specimen in test run No. 13, safety bars were installed (figure 4.16) to prevent a possible complete overturning of the

panel at failure. The loading eccentricity used was 1/6 the wall thickness of 3 in (76.2 mm).

Other details of the test setup duplicated run No. 13 where applicable; as in run No.

13, load bearing was directly on the surrounding aluminum frame. In summary, the major

difference between this run and run No. 13 was the use of flat load bearing at the

bottom as opposed to fulcrum load bearing in run No. 13. In progressing by load increments

of 500 lb/ft (7.3 kN.m), popping noises suggestive of incipient failure were heard at 8750

and 9800 lb/ft (127.7 and 143.0 kN/m). Failure occurred at 10,950 lb/ft (159.8 kN/m) by a twisting separation of the aluminum frame from one edge, near the bottom of the wall, followed

by a tensile crack and spalling of a large wall section (fig. 4.16). Also visible in fig.

4.16 is the faulty void in the foamed urethane core which caused the failure at that

location. Consequent displacement of the wall as a whole was limited to a lateral shift

of the bottom end (fig. 4.16). Maximum deflection of the panel at failure was nearly 1 in

(25.4 mm)

.

4.19 Test Run No. 19 (GFRP) - The specimen for this test was a fiber glass-reinforced

panel which is described in section 2.1.3. For this test the loading eccentricity was adjusted to one-half the wall thickness, placing the load line in the plane of the

interior surface. Except for the greater eccentricity the test setup was the same as that for run No. 17. During the test, oblique flood-lighting was used to give prominence

to surface deformations (fig. 4.17). The panel was loaded in increments of 250 lb/ft

(3.6 kN/m) to a maximum of 4750 lb/ft (69.3 kN/m). Maximum deflection at failure took place

gradually by bond separation of the facing on the compression side near the top. The three

photographs in figure 4.17 show the panel as maximum load was reached and upon subsequent failure.

4.20 Test Run Nos. 20-25 (WFTH) - In performing the next 6 tests, additional objectives

included observing the effect of a difference in the method of testing on the general

performance and mode of failure of a given type of construction, and observing the

reproductibility of results in replicate tests. To do this, 2 groups of 3 test runs were performed. Test run Nos. 20-22 permitted direct load bearing on the wall panel

facing elements; test run Nos. 23-25 prevented it. These last 6 test runs made use of

wood-frame construction panels described in section 2.1.1. The panels, designated WFTH,

contained 3 studs spaced symmetrically about the centerline of the wall at nominal 16-in

centers. The 3-stud design was chosen over the 4-stud (WFFR) arrangement as being more representative of a 4-ft (1.2-m) width of this type of construction. In such a 3-stud

specimen the outermost 8 in (0.20 m) , of the facings at both edges of the panel were left

unsupported. To compensate for the lack of continuity afforded the facings between

38
studs, the vertical edges were braced by wood spacers. The spacers, 3/4 x 1 1/2 in (19.1

X 38.1 mm), were cut to match the stud depth, 3 1/2 in (88.9 mm), and attached by

single, centered 4d wire nails through each facing (figure 4.18). The specimens used in

the 6 tests were alike in all respects except one. The 3 panels for test run Nos. 20-

22 had facings which were flush with the bearing surfaces of the top and bottom wood

plates while the panels for the remaining 3 test runs (Nos. 23-25) had their facings cut

back 3/8 in (9.5 mm) from the bearing surfaces at top and bottom.

The loading procedure, using a loading eccentricity of t/6 based on the gross wall

thickness, was the same for all 6 tests and was as described in section 2.2, except that

in the following tests the upper and lower containing angles on the interior side (which

became concave) were spaced 1/2 in (12.7 mm) from the wall surface (figure 4.19) to prevent unrealistic localized damage, yet contain the wall-end if necessary. In some of

these tests, it was necessary to increase the 1/2-in (12.7-mm) space during the test by

repositioning the angles to avoid contacting the bowed wall. The exterior angles tended

to become tangent to the convex wall surface at the bearing ends as curvature developed

and did not create a problem. The load increment, at which loading was stopped for

making measurements, was 500 lb/ft (7.3 kN/m)

.

The instrumentation was the same for all 6 tests and was of the same general arrangement

described in section 2.3 but with the following modifications (see figure 4.18). In addition to the 4 compressometers used In earlier tests (e.g., test run No. 1), 2 others were used —one at the middle of each face, offset 3 in (76.2 mm) from the vertical

centerline in opposite directions. Lateral deflection measurements were limited to midheight locations. In addition to the 2 edge-def lectometers , 2 others were used, one next to each mid-face compressometer , but 3 in (76.2 mm) to the opposite side of the

vertical centerline. The mid-face compressometers, as well as the def lectometers , on opposite faces of the panel were located diagonally with respect to each other. The

gage length of all face-mounted LVDT support poles was 88 in (2.2 m) and that of the 2 edge-mounted def lectometers , was 94 inches (2.4 m)

.

Tes t Run Nos. 20, 21, 22 further ensured full bearing of the already flush facing

edges by having the ends of the panels capped across the gross thickness with a thin

embedment of high-strength gypsum (figure 4.19). Capping was accomplished by gravitybedding each end of a panel, alternatively, against a floor-based, oiled steel plate.

Performance of the specimens in these three tests followed reasonably similar patterns.

Evidence of failure in test run Nos. 20, 21 and 22 is illustrated respectively by aftertest figures 4.19, 4.20 and 4.21. As seen in table 1, maximum load capacities were

similar but maximum deflections were not. Compression failures of the gypsum wall board

at the tops of the specimens in test run Nos. 20 and 21 are seen in figures 4.19 and

4.20. The beginning of a similar failure was observed at the bottom in test run No. 2_,

39
but testing was terminated by splitting of a stud seen in the close-up of figure 4.21.

All three tests demonstrated crushing and rotation of the horizontal wood plates. This

type of damage is typical of such frame construction. The uniformly distributed, but

eccentric, load is concentrated on the ends of the studs which crush the contact surfaces

of the horizontal plates off-center, thus resulting in rotation of the top and bottom

plates

.

Test Run Nos. 23, 24, 25 were performed with deliberate easement of facing bearing

as described earlier in this section. However, to make a fair comparison of the 2 groups of triplicate tests the bearing ends of these panels (i.e., wood-frame plates

only) were also capped with gypsum to achieve comparable bearing (figure 4.22). Results

of these three test runs are illustrated by figures 4.22, 4.23 and 4.24 respectively.

The general performances of these 3 specimens were more similar, within a group, than were those of the facing bearing specimens as is illustrated by the superimposed loaddeflection curves in figure 4.25. The curves are the x-y monitor records for one ram

and one edge mid-height def lectometer for the earlier stages of both groups of tests

before localized damage excessively influenced performance. Table 1 shows the similarity

in maximum load capacities of tests 23, 24 and 25. Wall panels in these three tests all

experienced closure of gypsum board bearing-relief cut-backs as a result of crushing

rotation of the wood plates (see figs. 4.22, 4.23 & 4.24). Test run No. 23 was terminated

after load bearing of the gypsum board was followed by cracking of an outer stud at midheight (figure 4.22). The mid-height crack in the gypsum board was secondary. Extra

spacer blocks, visible at mid-height, had been installed to bridge handling damage

present at one edge. The damage was not considered contributory to failure. The

cracks which are visible in the top wood plate in figure 4.22 are shrinkage cracks.

Test run No. 24 repeated closely the performance of No. 23. Figure 4.23 shows the

interior stud which split, as well as other evidence of similar behavior. Test run No.

25 also repeated, generally, the performance of the two preceding tests; however, no sudden failure occurred. The load reached a maximum value beyond which it gradually

decreased. The test was terminated because the deflection exceeded the translation

capacity of the LVDT's and because of the forced displacement of the face-mounted support

tubes. This forced displacement was caused by the bowed exterior face at mid-height

(figure 4 . 24) . , , ' ,

' • : ^

As an example of the type of load-deflection plot which can be obtained by computer

programming, figure 4.26 presents data obtained in test run No. 24. East and west sides

refer to panel edges; south face refers to the interior or concave surface.

Digital data provided by the computer pro

last 6 tests (Nos. 20-25) to determine the fea

measurement locations on wall test specimens.

cessing program were also examined for the

sibility of reducing the number of instrumented

Average values of the 4 "edge"-compressometer3

40
were compared with the 2 mid-face compressometers and average values of the 2 edgedef lectometers were compared with each of the 2 mid-face def lectometers . Conclusions

based on these comparisons are given in the following section.

41
1

CO

2

3

5

l<3

4'-0"

± /2"LVDT

GAGE LGTH ~ 88"

II^IEAR FACE) 13 (NEAR FACE) A

12PPP.FACE) UPPP-FACE)

6

7

EH

9

(CH

10 1^

i 1/2"LVDT (TYP.

SUPPORT TUBE

± 1" LVDT (TYP.

± 3" LVDT (TYP.)

± 1" LVDT (TYP.)

± '/2"LVDT (TYP.;

Figure 4.1 - Instrumentation setup for measuring wall shortening

and deflection.

42
-V

SPRING-

^\ WW rw ww \ww \ WW t \ww

I \ ww

WWWWWKWWXW^ WWWWWNNWWWN WNWW\wk\WWW> WWWWWKW\WWN W\WWW\\W\WWN WWWWwkWWWXN

Figure 4.2 - Details of L^TDT-core contacting wall-ciounted reference plate,

43
Figure 4.3 - Test run No. 4 (WFFR)

.

44
Figure 4.4 - Test run No. 5 (WFFR)

.

45
Figure 4.5 - Test run No. 6 (WFFR)

46
Figure 4.6 - Test run No. 7 (WFFR)

.

47
Figure 4.7 - Test run No. 9 (WFFR)

.

48
Figure 4,8 - Test run No. 10 (STLS)

49
Figure 4.9 - Test run No. 11 (STLS)

.

50 ,
Figure 4.10 - Test run No. 12 (GFRP)

.

51
52
Figure 4.12 - Test run No. 14 (GPHC)

.

53
Figure 4.13 - Test run No. 15 (STLS)

.

54
Figure 4.14 - Test run No. 16 (GPHC)

.

55
Figure 4.15 - Test run No. 17 (GFRP)

.

56
Figure 4.16 - Test run No. 18 (ACUP)

.

57
Figure 4.17 - Test run No. 19 (GFRP)

.

58
Figure 4.18 - Typical setup of test run Nos. 20 to 25 (WFTH)

.

59
Figure 4.19 - Test run No. 20 (WFTH, face bearing).

60
Figure 4.20 - Test run No. 21 (WFTH, face bearing).

61
Figure 4.21 - Test run No. 22 (WFTH, face bearing).

62
Figure .11 - Test run No. 23 (WFTH)

.

63
Figure 4.23 - Test run No. 24 (WFTH)

.

64
Figure 4.24 - Test run No. 25 (WFTH)

.

65

PR0T0 TYPE WALL TEST SPECinEN 20 TEST 1 VR-65

AUGUST 1,1974

UJ o

o

on _1

(_) ID

cr

+

o

o

°0.00 0.20 0.40 0.60 0.80

LVDT WEST SIDE MID . DEFL

.

1.00 1.20 1.40

INCHES

1 .60 1 .80

0.00 0.20 C.40 0.60 0.80

LVDT S0UTH FACE MID. DEFL

.

1.00 1.20 1.40

INCHES

I .60 .80

O I

^

f 1

1— -.:C 0.20 0.40 0.60 0.80

LVDT EAST SIDE MID . DEFL

.

1 .00 l'.20 l'. 40 INCHES

I'.ec r.80

Figure 4.26 - Computer-plotted load -deflection curves, test run No. 24.

67
5. SUMMARY AND CONCLUSIONS

5.1 Summary - An experimental and analytical investigation of the primary factors

involved in the test of wall panel prototypes under axial compression loading was reported.

In order to establish the test parameters that warranted investigation, a survey of the

literature on performance testing and a canvass of the members of an ASTM Task Group

that is concerned with testing of vertical structures was conducted. Several test factors which were of common concern were identified and a research plan was established

as a result of the survey. Twenty-five laboratory tests were conducted on five types of

wall panels to fulfill the objective of developing an improved method of testing for

compressive load resistance. The wall panel specimens were loaded incrementally to failure, while axial and transverse deformation responses were measured with electromechanical gages. As the tests were developmental in nature and not intended to evaluate

the relative resistance capacity of the types of construction, only selected results were presented herein. The proposed standard test method was written according to the

recommended format for ASTM Standard Methods and is presented as a part of this report.

The proposed method describes the apparatus and procedure to be used for applying either

a specific test load or an unknown maximum test load to a wall panel specimen which is a prototype of a designated wall construction.

The principal revisions of the existing standard method for compression testing

are: (1) a provision for variable eccentricity of loading through the use of adjustable

loading fixtures, (2) the incorporation of a procedure for selecting a load distribution

assembly that applies an approximately uniform load to the top of the wall panel specimens

and (3) a change in the end restraint condition from flat-end to pin-end.

A computer-aided analytical study of the variables affecting the degree of nonuniformity of loading was conducted. The conditions of the technical problem were found

to have a theoretical analogy in the theory of beams supported on elastic foundations.

The theoretical case of a beam of finite length, with free ends, being subjected to a number of concentrated loads relates to the laboratory testing of a wall panel specimen

to which concentrated loads are applied through the use of a distribution assembly.

Since it is often desirable to optimize the number of concentrated loads and the

stiffness of the distribution assembly, the objective was to derive a mathematical tool

to aid in making these selections. Using Hetenyi's solutions of the basic differential

equation for different loading cases, a mathematical procedure was derived and a computer

program was- written to perform the calculations. The procedure requires the input of

several variables: (1) the stiffness of the proposed load distribution assembly, (2)

the number and location of the concentrated loads and (3) the maximum variation, from

ideal uniformity, that will be allowed. The output from the iterative calculations is

the value of the maximum axial stiffness (i.e., foundation constant) that is permissible

68
for testing with the proposed distribution assembly, without exceeding the stipulated

maximum allowable variation from uniformity. The proposed test method in section 6 contains two useful tables that resulted from this study. The first table (6.A.1)

contains experimental values of foundation constants for panels representative of some typical wall constructions. The second table (6. A. 2) illustrates typical output from

the computer program as generated from the input of five different load cases, two different wall panel widths and seven different stiffnesses of distribution assemblies.

The Fortran V computer program that was used to generate this output is printed in its

entirety in Appendix A.

The ASTM Standard E72 specifies an apparently arbitrarily chosen procedure for

obtaining the eccentricity of loading. During this study the evolution of ASTM E72 x-ias traced, but no insight was gained as to the rationale for designating the single eccentricity

of one-third the wall thickness value. However, it x^as inferred that the one-third

fraction was conceived from the postulate of a kern radius that is explained in discussions

on eccentrically loaded compression members. The question of what is the true eccentricity

at the end of a wall panel is a complex one due to such factors as the relatively thin cross sections, the inherent inaccuracies of loading fixture positioning and the heterogeneous

composition of most types of wall construction. On the basis of assumed composite

behavior of these heterogeneous panels, it is possible to compute the theoretical core

or kern radius for a given type of construction. As an analytical exercise, the core radius was computed for three commonly used types of wall construction and the values were compared to the eccentricity derived by the ASTM E72 procedure.

A problem associated with standard test methods for building components in general

is how to utilize the test results in a design or evaluation decision process. In this

context, it is important to determine, prior to testing, the type of test that is to be

conducted. That is, the evaluator must establish what kind of prediction he desires to make, about the behavior of the actual component, on the basis of the test results. In view of the fact that tests for compressive load resistance are usually conducted on representative samples (i.e., prototypes) of the actual wall panel construction, it was

concluded in this study that the evaluator would desire to make a highly confident

prediction (i.e. with a probability near 1.0) about the performance of a large proportion

of the actual walls constituting the population. A study of the statistical parameters

commonly used to describe test results, revealed that the use of one-sided tolerance

limits was appropriate for this purpose. The use of one-sided tolerance limits was recommended in the proposed standard test method and the step-by-step procedure is

presented in section 6.9.3.

5.2 Conclusions - Many of the conclusions based on the observations and results of thi=^ investigation were incorporated into the proposed standard test method which follows in

69
section 6. The more notable findings acquired from both the experimental program and

the analytical exercises are presented as follows:

1. Wall panels of multi-component (i.e., with facings, stiffener and perimeter components)

construction exhibit localized, and generally, heterogeneous response when they are subjected to eccentric compressive loads. Consequently, the number of displacement

gages cannot be reduced by replacing two or more gages with one gage located at the

centroid of the several gages. In choosing instrument locations, a judgement should be

made as to the influence of expected localized behavior on the measurements. Observations

of such localized behavior should be reported with the test data.

If a wall panel specimen is expected to flex as a slender column, deflection gages

should be mounted on the edges of a wall specimen to approach alignment with the neutralsurface (N.S.) location. Nevertheless, even if two gages are so mounted along opposite

wall edges, and their data is subsequently "averaged" to approximate overall behavior,

the individual records should also be reported. Furthermore, it is to be noted that if

it is physically necessary to mount the def lectometers over a gage length which is less

that the full height of the specimen, the deflection measurements must be given additional

consideration. If the specimen gives evidence of beam-column action throughout its

length, an appropriate classical beam-column deflection formula should be used to extrapolat

the deflection measured over the shorter gage length to a value representative of the

full specimen length or to establish that the error incurred by the length difference

involved can be tolerated. If, on the other hand, the deflection is influenced by local

deformations, so that the shape of the specimen cannot be approximated mathematically,

the def lectometer gage length can only be made to approach the full length as nearly as possible, and the deflection measurements reported with accompanying qualifying comments.

When displacement gages must, of necessity, be mounted in pairs on opposite faces

of a wall specimen for the purpose of averaging the data (e.g., measurements of wall

height shortening or of wall deflection), the distances of both instruments' points of

suspension from the neutral surface must be equal. This requirement is necessary to obviate tedious arithmetic corrections which must be made when opposite instruments are mounted at unequal distances from the N.S.; when the opposing gages are mounted at equal

distances from the N.S. and their measurements are averaged, there is an automatic

compensation of the errors which are introduced into each instrument by rotation of the

facing-based mountings as the wall undergoes flexural response.

2. As demonstrated in figure 4.25, participation of wall panel facings in resisting

compressive loads can appreciably affect the panel's stiffness characteristics as well

as its strength (see table 1) . Therefore it is important to establish the extent to which the various components of such types of wall construction are intended to contribute

to the structural performance of the wall in practice, so that laboratory testing can be

conducted accordingly. For example, a multi-component wall construction may have facings

70
which are not intended to be subjected to direct vertical load bearing at their ends.

Then, the test panel should be prepared in such a vay to ensure that the ends do not

bear against the loading fixtures. Also, the wall cross section to be used in calculating

the centroid must be determined on the basis of the expected contribution of the individual

components to the flexural resistance of the wall panel.

3. labile the standard test method for evaluating wall panel resistance to compressive

loading should specify eccentric load application, designating a single, arbitrary

eccentricity to be applicable to all tj'pes of wall construction is not recommended.

Rather, the loading fixtures should be adjustable to facilitate a reasonable range of

eccentricities. The testing agency can make the final decision on test eccentricity

depending on the framing details of the actual building.

4. As a practical alternative to a conplex and expensive experimental procedure to locate the centroid of a given wall cross section, it seens reasonable to assume composite

resistance contributed by the full cross section and then locate the centroid by the

technique of transformed areas. Once the centroid of the cross section is located, it can serve as a reference for establishing the test eccentricity of loading. Either, the

kern radius can be calculated and used as the designated eccentricty or some other value

based on the framing details of the actual building can be specified.

5. The range of deviation percentage obtained from the three examples presented in

Appendix B extended from 2% (Example 1) to 38% (Example II) . Such a broad range suggests

that the use of the fixed value, t_/3, as measured from the inside face, in place of the

analytical procedure of establishing the eccentricity by computing the kern radius needs

further study. Tne agreement between the t^vo approaches is dependent upon the stiffness

of the facing materials relative to that of the core material. Moreoever, because the

interior facing material for this type of construction is usuallj' gypsum wallboard, the

agreement is strongly dependent upon the stiffness of the exterior facing material

relative to that of the core material.

6. Numerous observations regarding instrument usage, which were mentioned in section 4 can be suimnarized as follows: Measuring instruments must be mounted and used with

cognizance of surrounding conditions which might be adverse to the functioning of the

instruments. The detector of a displacement gage must be accurately aligned v^Lth the

direction of the component of the specimen displacement being sought. Also, provision

must be made in the mounting procedure to neutralize the effect on the gage of unwanted

components of specimen displacement. The unwanted components often prevent proper functioning

of the gage. In many instances, these difficulties can be reduced by suitably" mounting

the gages on the specimen rather than on surrounding reference bases such as the test

reaction frame or the test floor.

71
7. Since the end conditions of load bearing walls vary widely in practice and cannot

usually be simulated realistically, it is recommended that wall compresssion tests be

conducted with eccentric loading applied through pin-end conditions at both ends. This

is recommended over a pin-flat combination from the standpoint of being conservative,

and of ease of modelling for analytical evaluation. As an illustration, for the conditions

of a "partially restrained" flat bottom and pin-end top, the location of the point of

maximum transverse deflection is, in general, not well established, while for the pinpin end conditions the maximum transverse deflection occurs at mid-height.

8. Because the ends of a wall specimen supported by two pinned ends may undergo substantial

rotation during testing, it is necessary to specify fixtures that can provide adequate

containment of the wall ends. However, the fixtures must be employed with caution in

order to avoid damaging the specimen through excessive restraint.

9. Shadow lighting and quadrilling of the faces of a specimen can be used to facilitate

early detection of certain modes of failure (e.g., the localized buckling of the thin

skins used in some sandwich panel construction)

.

10. Safety restraints should be used around specimens whose expected brittle behavior

at failure would be hazardous to personnel and test equipment.

11. It is not possible to recommend a specific rate of loading applicable to a variety

of wall construction types on the basis of the laboratory or analytical investigations

reported here. The differences in response characteristics exhibited by wall panels

possessing different material properties would render such an undertaking impractical.

A basic requirement when selecting a nominal rate of loading is that the rate should not

be so fast as to cause the corresponding deformation to significantly lag the application

of the load. \

'

' " -

72
6. PROPOSED 51.^;:.^-^; i^zihcd of test for compressi\^ strength of

WALL CONSTRUCTIONS, ASTM DESIGNATION E- —

With the continuing development of building technology, stimulated in part by new

methods and materials of prefabrication and by emerging performance criteria, there is an attendant need for accurate technical data on the strength and rigidity of presentday wall constructions. It is the purpose of this test method to provide an improved

systematic procedure for obtaining engineering data on the strength and rigidity of wall

constructions which are of value to designers, producers, consumers, and building

officials interested in the perfortnance of bearing-wall constructions,

6.1 Scope

6.1.1 This nethod cf -esr describes a procedure for detemining the perfor-nance of

load-bearing wall ccnstruction segcents under the action of vertical, eccentric, compressive,

static loading. ~r.e -erhod describes the apparatus and procedure to be used for applying

either a specific tesr load (proof or acceptance test) or an unknown maximum value test load (failure tesc) to a prototype specimen. Tailure is defined as the inability to support a specified tesr load or to fulfill a specified perforziance requirement.

6.2 Summary ci Method

6.2.1 A wall segment oriented in a vertical position is loaded by a row of hydraulic

rar:s acting vertically in the plane cf the wall segment. The line of rams is eccentric

to the centroidal axis of the wall's cross section so that loading tends to cause outof-plane bending as well as other accompanying displacements. Load and displacements

are monitored autographically to detect critical occurrences in performance,

6.3 Significance

6.3.1 The structural resting of complete buildings is expensive, time consuming and

sometimes indeed impossible. Such tests of integrated elements in a whole structure

have the further disadvantage of being terminated by the failure of the weakest element.

Usually the only practical approach involves testing a small sample of wall segments,

using a test method which approximates service conditions.

This proposed standard test method has been submitted to the American Society for

Testing and Materials (ASTJI) for consideration as an AST?' standard. As such it has been

prepared as a completely self-contained document . It is to be considered as a review

draft in that it ''rill no doubt undergo several revisions before being adopted as a standard.

73
6.3.2 Current building codes do not specify allowable deflections for walls under

vertical load. Nevertheless, the need often arises for comparing the strength and

stiffness of a wall system of unknown performance with that of a wall of established

performance. This test method serves to determine the load carrying characteristics of

a wall segment subjected to vertical loading which is eccentric within the dimension of

the wall thickness. Since the line of loads is applied at each end through a fulcrum,

actual end bearing conditions are not simulated. No attempt is made to achieve such

simulation because actual end conditions are a function of type of construction and must

be considered as a variable. The test report must, therefore, address the differences

between end conditions used in the test and those of the wall in the actual structure.

The test results will generally be on the conservative side in the evaluation of the

relative strength or stiffness of wall constructions. In this sense the method is a rating test. Also, these procedures can be employed toward the objective of establishing

either a load factor-of-saf ety , given a certain design load or an allowable load, given

a safety factor. . .

'

; ,

-

6.4 Apparatus

6.4.1 The apparatus shall be assembled as shown in fig. 6.1. and shall conform to the

detailed requirements for component parts prescribed in 6.4.1.1 through 6.4.1.7.

6.4.1.1 Testing shall be performed within a test frame which has a stiffness in the

direction of loading that is at least 100 times greater than that expected for the

specimen. , .

,

•

< . , .

6.4.1.2 A loading system employing hydraulic rams which are driven by a motorized pump

shall be used to apply a distributed load to the top of the specimen along its width.

The pump shall be equipped with regulators capable of controlling load application and

of maintaining the load. The least number of rams (points of load application) shall be

determined with the aid of tables 6.A.1, 6. A. 2 and the accompanying text of Appendix

6. A. A hydraulic testing machine of adequate size and load capacity may be used for

load application provided due consideration is given to the uniform distribution of

loading.

6.4.1.3 An electrical resistance type load cell (dynamometer) shall be mounted in

tandem with each ram to measure the applied load. See Paragraph 6.5.1 (under Safety

Precautions)

.

6.4.1.4 A 135°-V-grooved steel plate shall be used as a receptacle for a knife-edge

fulcrum and as a bearing plate for the top of the wall specimen. Machining of this plate

and all other metal parts shall be performed in accordance with good machine shop

practice. The position of the bearing plate shall be adjustable across the thickness of

74
75
the wall specimen to achieve the designated eccentricity of the loading fulcrum. Structural

angles which can be adjusted into position and bolted to the bearing plate shall be used

to contain the top of the specimen laterally.

6.4.1.5 A steel plate welded to a 90°- knife-edge fulcrum shall be used to distribute

the load from the hydraulic ram system uniformly along the width of the specimen.

Welding of the knife-edge fulcrum to the plate shall be performed according to -the requirements of American Welding Society standards and American Institute of Steel

Construction specifications. Continuity of seating of the fulcrum in the V-groove shall

be obtained by establishing that the surfaces are in contact at the 1/10 (of total

width) points as a minimum.

6.4.1.6 A corresponding assembly of steel plates, knife-edge fulcrum and angles shall

be used in an inverted arrangement at the bottom of the wall specimen.

6.4.1.7 A def lectometer shall be mounted on both vertical edges of the wall specimen to measure mid-height deflection. These def lectometers should be electromechanical so that

load and deflection can be monitored continuously and autographically by an X-Y plotter.

The def lectometers shall be mounted over the longest span possible, approximating full

height, on the specimen itself (i.e. not mounted on the floor or test frame) in order to measure net deflection and eliminate effects of test set up movement. Alternatively,

the def lectometers may be dial micrometers. It should be noted, however, that this

alternate instrumentation does not allow continuous monitoring of the deflection response.

6.5 Safety Precautions

6.5.1 All components of the loading system, such as rams, load cells, plates, etc. must

be inter fastened and/or suspended from the reaction frame so that they can be supported

without a specimen present in the test position.

6.5.2 At the start of the test, the vertical legs of the structural angles used for

containment of the ends of the specimen must be in full contact with the surface which

is designated as the exterior face (face which is furthest from the eccentric load) of

the wall. The angles on the interior face of the wall should be spaced at a suitable

distance from the wall in order to avoid gouging of the interior surface of the wall by

the vertical legs of the angles during the test. If rotation of the wall-end fixtures

is enough to cause closure of the allowed space, the interior angles must be readjusted

during the test to prevent contact and possible crushing of the interior wall surface.

6.5.3 Caution must be exercised against injury to personnel, and damage to equipment by

unexpected release of potential strain energy accumulated during the test.

76
6.6 Test Specimens

6.6.1 Wall specimens shall be representative of the construction to be used in service.

The height of the specimen shall conform to the height of the wall in actual use. The

width of the specimen shall be a whole number multiplied by the spacing of the principal

vertical load-bearing members and shall extend from mid-space to mid-space, except for

prefabricated panels, for which the width shall be as manufactured. To the extent

practicable, in accordance with these requirements, specimens shall be nominally 4 ft

(1.2 m) wide.

6.6.2 Compression tests shall be made on a sample consisting of at least five similar

specimens

.

6.7 Conditioning

6.7.1 Specimens shall be in a general state of readiness to be placed in service to undergo design loads and before testing shall be exposed for 7 days to temperature and

humidity conditions equal to those of the testing laboratory (e.g., 73 + 3°F, 50 + 5%

R.H.). Cooditioning requirements for specific materials which might be damaged by

exposure to other environmental service conditions shall be in accordance with appropriate

specifications

.

6.8 Procedure

6.8.1 The specimen shall be tested in compression as a beam column having fulcrum ends

at top and bottom (fig. 6.1). Compressive load shall be applied to the top, uniformly

along a line parallel to the faces of the wall. The eccentricity of loading shall be

equal to the theoretical kern radius of the cross section, unless the eccentricity

dictated by the actual framing details is known and used. The reaction fulcrum at the

bottom shall have the same eccentricity.

6.8.2 Load shall be gradually applied to the specimen in increments. The size of the

increments shall be chosen so that no more than 1/10 of the specified test load is

applied during each increment.

6.8.3 Load shall be applied continuously (i.e., continuously during each increment)in

a manner that effects a nominally uniform rate of deformation. In the absence of

loading rate guidelines, it is recommended that the rate of loading during each increment

not exceed 1/10 the specified test load per minute.

77
6.8.4 The first set of load and deflection readings shall be recorded prior to the

application of any test loading. These initial load readings shall serve as reference

points for all subsequent measurements. Individual load cells and def lectometers may be

calibrated for visual reading with a digital voltmeter or may be read and recorded

automatically. One load cell and one def lectometer shall be used for autographic

monitoring of the test by an X-Y plotter.

6.8.5 Load shall be increased to the end of the first increment and the load and

deflection measurements shall be recorded in accordance with paragraph 6.8.6. The

recording procedures specified in paragraph 6.8.6 shall apply for all subsequent observations.

6.8.6 Load and measurements shall be recorded upon reaching the end of each specified

increment of loading. Having maintained the load at the specified magnitude for a 5-

minute period, load and deformation measurements shall be recorded again. When the

loading is decreased, the load and deformation measurements shall be recorded instantaneously

upon reaching the initial load level. After a recovery period of 5 minutes, the set of

readings shall again be recorded. The schematic load-time plot in figure 6.2 illustrates

the loading and unloading cycle with the recording points denoted by dots.

LOAD

TIME

AT^ 5 MINUTES AT, 5 MINUTES

Figure 6.2 - Load-time schematic diagram.

6.8.7 Load shall be increased in specified increments until the test load is reached.

6.9 Calculation of Results

6.9.1 A load value at any test stage shall be calculated by summing the load cell net

values and dividing by the width of the specimen, (lb/ft, N/m)

78
6.9.2 Tne lateral deflection at ar.y stage shall be calculated as the average of the two

def lectoneter net readings. (in, n)

6.9.3 Test results shall be calculated as follows:

a. Obtain results, for a given para-eter such as naximun load, riaxisun deflection,

deflection at allowable load, etc., froE five, or aore, specinens : x^, x^ , x^,

X, X. ... .X

^, D n

b. Calculate the sanple average from the data obtained:

- 1 ? X = — _ X. ^ 1=1 ^

c. Calculate the sample estimate of the standard deviation:

I (X - x^)-

d. Establish tolerance limits to satisfy the degree of con^fidence that is desired.

General fonnulation: Tne probability is v (e.g., 0.95) that at least a proportion ? (e.g., 0.90) of a population 'id.ll be greater than x - ks (or

less than x -r ks) where x and s are esti'^ates of the mean and standard deviation

calculated from a sample of size n (e.g., 5). The value of k (e.g., 3.^07) is

obtained from a table of factors for one-sided tolerance limits for normal

distribution.

6.9.4 A sample set of calculations using the procedure outlined in paragraph 6.9.3 is presented as follows:

a. The transverse deflection (x) at a given allowable load was measured for five (n)

wa_^ specimens

.

b. Tr.e sample average calculated from the data is x = 0.1260 in.

c. Tr.e calculated value of the sample standard deviation is s = 0.00359 in.

d. Use a table containing factors for one-sided tolerance limits for normal

distribution to calculate the value of deflection (x ) below which we mav

u predict with 95:i confidence that 90% of the population will lie. Therefore

let ? = 0.90 and v = 0.95.

Tor n = 5, V = 0.95 and ? = 0.90, k = 3.407

X = X -i- ks

uX = 0.1260 -H 3.407 (0.00359)

uX = 0.1260 + 0.0122 = 0.1382 in ^ 0.138 in

u

79
6.10 Report

6.10.1 The report shall include the following.

6.10.1.1 Dates of the tests and of the report.

6.10.1.2 Statement that the tests were conducted in accordance with the prescribed

methods. Deviations from these methods shall be described.

6.10.1.3 Identification of the sample specimens, including manufacturer, source, physical

description, detailed engineering drawings, photographs and other pertinent information.

6.10.1.4 Detailed information of test set-up including engineering drawings and photographs

to make possible the duplication of test set-up by others.

6.10.1.5 Description (in addition to photographs) and interpretation of mode of failure.

6.10.1.6 Force - displacement graphs or other (if applicable) graphic, test progress

records (such as stress-strain curves)

.

6.10.1.7 Tables of test results (for various

deflection at allowable load, etc.) including

deviation and tolerance limits calculated for

parameters such as maximum load , maximum

sample average, sample estimate of standard

stated confidence level (cf. 6.9.3, d) .

: ':11V .i

80
6. A Appendix - Designing the Test Load Distributing System

6.A.1 Uniform test load distribution - An approximation of a uniformly distributed load,

parallel to the plane of the wall test specimen can be achieved by using several hydraulic

jacks to apply concentrated loads to a load distributing beam which, in turn, transfers i he

total load r.^ the top of the wall The greater the number of ^acks and the sciffer the

distributing beam, the more uniform will be the wall load. Restrictions on test site space

and economy are practical considerations which will limit the selection of the stiffness

(EI) of the loading beam and the number of jacks. After a decision has been made regarding

the maximum variation from a uniform load condition that can be toleiated, a computer

program can be used to investigate combinations of the number of loads, their placement and

the distributing beam stiffness (EI) that will provide the tolerable load distribution on a test wall of known or estimated stiffness (foundation constant, K)

.

6. A. 2 Computerized solution to the problem - The computer program is designed to provide

solutions to the problem, considered as an application of the theory of beams supported on elastic foundations (in this case, a load distributing beam bearing along the top of the

test wall) . The basic theory and equations are found in "Beams on Elastic Foundation" by

M. Hetenyi, University of Michigan Press, 1946. The beam of length, L, has a flexural

stiffness, EI and is supported on an elastic foundation (wall) which exerts a distributed

reaction proportional to the vertical displacement, y, of the foundation. The beam is

loaded by n equal, vertical loads spaced at a distance, D, from each other and beginning at

a distance ,aD, from each end. Figure 6.A.1 shows such an arrangement. The object of the

computer program is to obtain a maximum foundation constant, K, (expressed in lb per in of

width, per inch of vertical displacement) so that the maximum absolute value of the variation of the distributed foundation reaction (wall load) from the average value, divided by

the average value, is equal to a prescribed upper limit, Al . However, because of computational difficulties it is not feasible to solve the problem exactly as stated, but rather to compute a foundation constant which makes the maximum load variation ratio greater than a lower limit, A2, but less than an upper limit, Al. Thus, as an example, the upper limit of the

maximum load variation ratio, Al, may be made equal to 0.10 and the lower limit of the maximum

load variation ratio, A?., may be made equal to 0.05 or some other value smaller than, but as close to Al as may be desired.

6. A. 3 Computer output - Each trial solution gives the stiffness of a wall which can be

tested by the combination of beam and load arrangement being considered (i.e., entered as program input), without exceeding the chosen maximum load variation. The distance of the

first and last loads from the ends of the beam, aD, may be varied to maximize the foundation

constant which can be accommodated. By estimating the stiffness of the wall which is to be

tested ,the user can select the most desirable test arrangement for which the computer gives

a foundation constant larger than that which was estimated for the test wall. To assist

the user in checking initial estimates of specimen wall stiffness (i.e., foundation constants),

table 6.A.1 provides such values derived from the testing experience of the sources indicated.

81
Tablci 6.A.]~ Experimental Values of Foundation Constants

" for Panels Representative of Some Typical Wall Constructions^^

PANEL DESCRIPTION i FOUNDATION REFERENCE ^„.„..,..x,.,.2/

INTERIOR FACING

CORE EXTERIOR

SHEATHING

CLADDING

OR VENEER

(See List of Refs. Below)j

[

(Ib/in/in)

Textured 0.02"

thick aluminum

3" paper honeycomb Textured 0.02"

thick aluminum

No. (1) 3.16 X lO'^

1/2" gypsum wallboard

2x4 - wood studs

(a 16" oc 1/2" Insulating

f Iberboard

1" X 4" air dried select

wood siding

No. (1) 4.72 X lO"'

1/2" gypsum wallboard

2x4 - fir studs

(? 16" oc 1/2" insulating

f iberboard Common face brick

No. (1) 5.21 X

10''

Glass fiber reinforced polyester

laminate

3 5/8" thick corrugated coreglass fiber reinforced polyester

laminate

Glass fiber rein- forced polyester

laminate

No. (2) 5.42-6.67 X lO''

Fiber reinforced

polyester; woven

roving

3" paper honeycomb

Fiber reinforced

polyester; woven

roving

1/2" gypsum wallboard

interior & exterior

No. (3) 7.34 X lO-'

1/2" gypsum wallboard

18 ga. galv. steel "Z" studs

at 24" oc

1/2" nail base

insulating

f iberboard

No. (5) pp. 5 and 8 7.81-9.06 X 10^

1/2" gypsum

wallboard

4" X 8" X 16" concrete block

4" common

face brick

No. (1) 8.68 X 10^

1/2" foilbacked gypsum wallboard

18 ga. galv. steel "Z" studs

at 24" oc

3/8" cedar plywood

exterior grade

No. (1) 11.58 X 10^

1/4" Philippine

mahogany plywood

1 1/2" expanded

polystyrene w/2x4

stringers (3 48"oc

5/16" douglas

fir plywood aluminum

cladding

No. (6) pp. 52-65 14.29-17.94 X IQ-'

1/4" fir plywood

2 1/2" poly- styrene w/ 2 1/2"

X 2 1/2" fir stringers at 48" oc

l/4"fir plywood -

>-

No. (1) 14.88 X lO''

8" med. strength brick-common Ajner. bond-joints not completely filled

No. (4) Wall AB,

Fig. 11 54.10 X 10^

8" med. strength brick —common Amer. bond —j oinr.s completely filled

No. (4) Wall AC, Fig. 17 61.60 X 10^

8" stone concrete block

No. (4) Wall AF, Fig. 42 66.6 X 10^

- 8" clay tile-tiles

laid on side

No. (4) Wall AE, Fig. 34 71.00 X

10"^

— The tabulated values of "foundation constants" are presented uith the intention of supplementing Tattle 6. A. 2. It should he recognized that this table has been derived from single sets of experimental data obtained by testing 8-ft higli prototypes of a variety of wall constructions uith generally high variability of performance. 1%e values presented are intended to indicate

orders of magnitude of axial stiffness and should not be construed to indicate absolute measure.

2/ . — The term "foundation constant", taken from the theory of beans on elastic foundations, is used herein as a measure of axial stiffness of wall systems. It is expressed in units of Ibf/in (of wall) /in (of deflection) . The foundation constants presented in this table were calculated by measuring the slope in the elastic range, of test curves that plotted axial Ion-, versus shortening.

Table 6.A.1 - Experimental values of foundation constants.

82
Table &.A.1 Continued - LisL References Cited Above

"Perfcrmance Criteria for Exterior wall Syst'^r.s," National Burea-.- of Standards

CJ.S.) Report 9817 , oy Staff of Building Retearch Division, April 1968, Table 5-3.

"Structural Tests on Housing Components of Glass Fiber Reinforced Polyester Laminate,"

Reichard, T. W. et al, NTIS PB 221-183 , National Bureau of Standards (U.S.).

April 1973, 90 pp.

"Structural Tests for a Housing Systez! Using Sand-^Tich Panels with G3rpsuin Board Facings,"

Greene, V. E. et al , NTIS ?3 21--336 , National Bureau of Standards (U.S.), Nov. 1972,

75 pp.

"Structural Prcperiies of Six >!asonry Wall Constructions," Ti'hitteaore , H. L.,

Stang, A. H. and Parsons, D. Z., National Bureau of Standards (U.S.), Building Materials

and Structures Report (BMS) 5, Novenber 1938, 31 pp.

"Report on Compression Tests of Prefabricated Wall Panels," University of Louisville

(IIR), Report No. 40208 , Mcintosh, W. R. and Snowden, J. R. , February 12, 1974.

"Structural and Materials Performance," Volume II HLi) Austin Oaks Project , Fowler, D. Iv. and Houston, J. T., Decez:ber 1971.

83
Table 6. A. 2 shows values of input and output for various trial solutions to the problem

of providing satisfactory test loading for a variety of circumstances. Input values are

the same for both the left and right halves of the table except for the edge distanceload spacing ratio. The number of load cases considered is 5, namely 2, 3, 4, 5 and 6 equidistant concentrated loads. The number of wall specimen widths considered loaded by

each number of loads is 2, namely 48 in and 96 in. The number of attempted beam stiffnesses

is 7; these values of EI represent a variety of loading beams such as steel rolled

2 sections and timbers. The tabulated values of EI (Ib-in ) are expressed as a decimal

to be multiplied by 10 raised to the indicated power which follows the plus sign. The

edge distance-load spacing ratio, a, (which indicates proximity of the outer loads to the wall edges) is 0.5 for cases in the left half of the table and 1.0 for the right

half. The stated values of upper maximum load variation (0.10) and lower maximum load

variation (0.05) indicate that, for the solutions obtained, the acceptable maximum

variation from uniform load distribution lies between 5% and 10%. For each combination

of (1) edge distance-load spacing ratio, (2) number of load points, (3) wall width and

(4) distributing beam flexural stiffness (EI) , the information and results are presented

in a single line of output under the column headings. The solutions (under column heading

FOUNDK expressed as a decimal to be multiplied by 10 raised to the indicated exponent)

give the range of specimen axial stiffnesses which can be tested by the corresponding

loading arrangements within the acceptable limitations imposed on variation from uniform

load distribution. It is intended that the range of values presented in table 6. A.

2

together with the illustrative foundation constants in table 6.A.1, assist the user in

determining a suitable loading arrangement for applying a satisfactorily uniform load to the specimen to be tested.

^FOUNDATION REACTION (FORCE PER UNIT

LENGTH OF BEAM) = (K){Y)

a D D D a D

L

Figure 6.A.1 - Beam on elastic foundation.

84
NUMBER OF LOAD CAS"? IS f, NUMBER OF LOAU ("aSFS IS b NUMRER OF WinTM<^ 1 2 NUI«:bER OF WIDThiS IS 2 NUMBER OF PEA-.' STIrfiFSSES IS 7 NUMiiEK OF REAM STI^mFSSES IS 7 EU6E DISTaNCE-LOAO SPACIfJG RATIO Ic .SO ^^''^ D I STAMCF-LO AD SPACING PATIO IS 1.00

*'AX. LOmP VA:.' I ATION 1=; .10 MAX. LCAP VAO I ATI OM IS LO*ER ''AX. LOA'^ VA- lATION I'^ ."5 LOWER •lAX. LOA'^ VARIATION TS

LO AOS wvinri-' EI FOUND'' LOADS i^ I DT^E

I

2 t8. 0 . 190U+08 . 3904 + 03 2 4 . 0

1 o n n J. n o . 1-*UU + UH 0 7 ^ (1 ^ n 0 2 18. 0 .7?00+08 . 15S9+04 2 46 . 0 . 7?oo + 08 . 3904+03

2 48.0 .1800+09 .3113+04 2 46.0 , 1800+09 , 1170+04

2 48. 0 .1600+10 . 3bo4+0? 2 48 . n , 1600 + 10 9277+04

2 46.

0

.2934+10 .6875 + 0=: 2 48 . 0 . 2934 + 1

0

. 1836 + 05

2 ta. 0 . ^990 + 10 .6875 + 0=; o 43

.

. 3090+1

0

, 2422 + 05

2 us.o .612U+10 .1250+06

o 4 8.0 .6120+10 . 3594+05

2 96.0 .1900+08 .2441+02 96 . 0 , 1900+08 .6103+01

2 96.0 . 7?00+08 .0764+02

o 96 .

0

. 7200+08 .2441+02

2 96. r . 1800+09 . 1953+03 2 96 . 0

1 n A A J A .1800+09 . 7324 + 02 2 96.0 . 1600+10 .2338+04 £ 96.0 . 1600+10 . 5856 + 03 2 96. 0 .?o?4+10 .3113+04

OC. 96 . 0 . 2034+1

0

• 1 170 + 04

2 96. 0 . ^'^90 + 10 •4663+04 C. 96.0 . 3000+10 . 1 559+04

2 96. n .6120+10 .6201+04

O 96 . 0 . 6120 + 10 . 2338+04

3 48 .

1^ . loOU+08 . 1 170+04 48,0 . 1900+08 . 1465+03

3 48 . 0 .7200+08 .4663+04 3 48.0 . 7?00+08 . 5856+03

3 48. 0 .1800+09 .0277+04 3 48 . n . 1800+09 . 1559+04

3 48. 0 . 1600+10 .1125+06 3 48 •

1^ . 1600+10 . 1230 + 05

3 43.0 .2034+10 .2250+06

•»3 48 , 0 . 2031++1 0 .2422+05

3 48. 0 . ^ogo+io .2500+06 3 48 , 0 . 3990 + 10 . 3594+05

3 48

.

.6120+10 .4500+06 48.0 .6120+10 . 4688+05

3 96.0 . 190U+08 .7324+0? 3 96. 0 . 1000+03 ,0155+01

3 96.0 .7200+08 .2929+03 3 96 . 0 .7200+08 , 3662+02

3 96.0 . 1800+09 .5856+0? 3 96 . 0 . 1800+09 , 0764+02

3 • 96.0 .1600+10 .4663+04

I 96 . 0 . 1600 + 10 . 7805+07

3 96. 0 .2934+10 .9277+04 3 96 .

0

.2034+10 ,1559+04

3 96.0 . ?9°0+10 . 1836+05 3 96. 0 . 3090+10 •2338+04

3 96. n . 6120+10 .1836+0=; 0 95 • 0 .6120+10 ,3113+04

H 48.0 . l<500 + 08 . 3694+04 4 48

.

. 1900+08 • 1953 + 03

48. 0 .7200+08 .1543+05 4 48.0 .7200+08 •7805+03

H 48.0 . 1800 + 09 . 3047+0 = 4 48 . r . 1800 + 09 • 1559+04

48 . r .1600+10 .2500+06 4 48.0 . 1600 + 10 • 1836+05

*> 48.0 .2934+10 .4500+06 4 48.0 .2034+10 •2422+05

48.0 . 3990 + 10 .5500+06 4 43. 0 .3000+10 . 3594 + 0=;

ItH 48.0 .'^lau+io .1000+07 4 48 . 0 .6120+10 • 6875 + 0=:

*f 96. 0 .1900+08 .2441+03 4 96 . 0 . 1900+08 • 1221 + 02

£ 96 . 0 . 7200+08 . 9758+07 i| 96 . 0 . 7200+08 •4383+02

n 96 0 1 fl n n J. n o 1 e <^ J. f

.

• 1 V50 + UU 4 1 Q n n a. A Q • 0764 + 02 96 0 1 c n n A 1 n • 1 836+0 5

4 96 • f: 1 n n X 1 n 11 'U + 04

QA p O O T / 1 J- 1 n

• 30*+7 + 0S ^ 96 . n 1 C Q ^ A «i • 1 30*3+04

^ n . 1 • j'-jy u + 1

0

• 3594+05 4 96 . 0

* Q Q n J. 1 n T 1 0 1 1. • 2338 + 04 4 96 .

0

•6120+10 • 6875+0? 4 96,0 .6120+10 • 4DDO+04

5 48 . 0

i n A i"! J. n rt . 1900 + 08 • 776^ + 0** 5 48 , 0 1 Q n n + 0 a • 1953 + 03

5 48 0

"7 ^ n n A ii Q

. '(^UU + Uo • 3 0U7+ 0 ? 5 48 . 0 7 ^ n n A ri a • ' r " U + U n 7 D A t J. A ^ • 'dOO + 03

5 48 • C . 1800+09 • 5875+0? 5 48 , 0 1 c n n J. n 0 "5 1 T Q A A • d JOO+ U 4 5 46.0 .1^00+10 • 9000+Of 5 4 8.0 1 c n n A 1 n • JoUU + i'J • 1 836+05

5 4*^ . 0 • '934+1

0

• 1100 + 07 5 48 • ^ 0 Q 1 ii a. 1 n

. 35^4+os

5 48.0 T Q o n J. 1 n

. .tWU + 10 • 1800 + 07 "S 43 • " , "^090 + \ Q ^ A a fi A n c 5 48 .6120+10 "5 A A A n T • 2£l0 U + U^ 5 4 3,0 •6120+10 . 6375+0 5

c3 96 .

0

. 190;)+08 •4881+03

c 96 . 0 . 1000 + 08 •1221+02

96 .

0

. 720U+08 • 1950+Oa

c 9b . 0 .7200+08 .48'^3+0?

cO 96 .

0

.1800+09 .4663+04 96 .

0

. 1 °O0+09 .1465+0'

e 96. 0 . 1600+10 .3594+0?

c 96 ,

0

. 1600 + 10 .1170+04 e 96 .

*> .2°34+10 .6375+0? 96 ,

0

.2934+10 .2338+04

5 96. 0 . 39°0+10 .1125+06 96 .

0

. 3000 + ir) .3113+04 c 96 . r .6120+10 • 1375 + 06 5 96 . o .6120+10 • 4663+Ou

6 48.0 .1900+08 .1543+0*^ 48.0 . looO+OS .2929+03

6 48.0 . 7200+08 • 5938 + 0? 6 48.0 70 n n A n Q • 1 1 70 + 04 6 48.0 . 1800+09 . 1375+06 6 48.0 . 1800+09 •2338+04

6 4b.

0

. 1600+10 . 1800 + 0*^ 6 48. n .1600+10 •2422+OS

6 48, 0 .?°34+10 . 3600 + 0"^ 6 48. 0 .2074+10 • 3504 + 05

6 48.0 . 3°90+10 .3600+07 6 48 . 0 . 7990+10 • 6675 + 05

6 48.0 .6120+10 .7200+07 6 4^.0 .<^120 + 10 •8750+05

6 96. 0 . 1900+08 . 97sa+03 6 96. r . 1000+08 • 1631 + 02

6 96.0 .^200+08 . 3a9i+ + 04 6 96.

o

.7200+08 .7324+0?

6 96. 0 .1800+09 . ^277+04 6 96.0 .1800+09 .1465+03

6 96.0 • 160 J + 10 .1125+06 6 96. r .1600+10 .1559+04

6 96.0 . ?°34+10 .2250+06 6 96.0 . 5031++ If) •2338+04

6 96.'' . 3990+10 .22S0+06 6 96.0 . 7900 + 10 •7113+04

6 96.0 .6120+10 .4500+06 6 96." .6120+10 •6201+04

Table 6. A. 2 - Correlation of compression-test setup factors for

uniform load distribution.

85
7 . ACKNOWLEDGMENTS

The authors acknowledge the valuable contribution made by the following persons:

Mrs. R. Hocker, Miss J. Reinhold, Clerk-Typists, performed the typing of the

several drafts of this report.

Messrs. L. Payton and M. Glover, Engineering Technicians, erected the test frame,

installed test hardware and prepared the test specimen.

Mr. J. Owen, Electronics Technician, executed the instrumenting of the specimen and

operated the data acquisition equipment during testing.

Mr. M. Lemay, Engineering Technician, performed most of the fabrication and machine

work.

Messrs. R. Williams, Physicist and F. Rankin, Supervisory Engineering Technician,

supervised the instrumentation-data acquisition activity and the laboratory-fabrication,

erection and specimen preparation activity, respectively.

86
8.0 REFERENCES

1. Yancey, C.W.C. and Cattaneo, I.E., "State-of-the-Art of Structural Test Methods for

Walls, Floors, Roofs and Complete Buildings," National Bureau of Standards

(U.S.)) Building Science Series 58 , November 1974, 133 pp.

2. Structural Properties of Lov-Cost House Construction , National Bureau of Standards

(U.S.), Letter Circular LC-502A, August 1937.

3. ^shittemore, H.L. and Stang, A.H., "Methods of Determining the Structural Properties

of Low-Cost Constructions," National Bureau of Standards (U.S.), Building >taterials

and Structures Report (BMS) 2 , August 1938, 18 pp.

4. ASTM E72-47T , "Tentative Methods of Conducting Strength Tests of Panels for Building

Construction," American Society for Testing Materials, Annual Book of ASTM

Standards, Part 4, 1949 edition.

5. ASTM E72-55 , "Standard Methods of Conducting Strength Tests of Panels for Building

Construction,

American Society for Testing Materials, Annual Book of ASTM Standards, Part

4, 1955 edition.

6. ASTM E72-61 , "Standard Methods of Conducting Strength Tests of Panels for Building

Construction," American Society for Testing and Materials, Annual Book of

ASTM Standards, Part 5, 1961 edition.

7. ASTM E72-61, "Standard Methods of Conducting Strength Tests of Panels for Building

Construction," American Society for Testing and Materials, Annual Book of ASTM

Standards, Part 14, 1965 edition.

8. AST>I E72-74, "Standard Methods of Conducting Strength Tests of Panels for Building

Construction," American Society for Testing and Materials, Annual Book of ASTM

Standards, Part 18, 1974 edition.

9. Shanley, F.R., "Strength of Materials," McGraw-Hill Book Company, Inc., New York,

1957.

10. Hetenyi, M.I., "Beams -on Elastic Foundation," The University of Michigan Press, Ann

Arbor, 1946.

11. Dorey, D.B. and Schriever, W.R., "A Philosophy on Loading Tests," presented at the

58th Annual Assembly of ASTM, Atlantic City, N.J., June 29, 1955.

12. Natrella, >Iary Gibbons, "Experimental Statistics, "National Bureau of Standards

(U.S.), N3S Handbook 91 , August 1, 1963.

-SCOW-VBS-DC

87
Appendix A - Computer Program for Load Distribution Analysis

A computer program designed to provide solutions to a problem based upon the theory

of beams on elastic foundations is described herein. The problem definition follows.

A beam of length L having a flexural stiffness EI is supported on an elastic foundation

which exerts a distributed restoring force proportional to the vertical displacement, y, of the foundation. The beam is loaded by n equal, vertical loads spaced at a distance, D,

from each other and beginning a distance, aD, from each end. Figure A.l shows such a beam. The object of the computer program is to obtain a maximum foundation constant K,

which may be expressed in Ibs/in/in so that the maximum absolute value of the variation of

the distributed foundation force from the average value, when divided by the average value, is

equal to a prescribed limit, Al . Because of computational difficulties it is not feasible to solve the problem exactly as stated, but instead a foundation constant is computed which

makes the ratio greater than A2 but less than Al . Thus, for example, Al may be made

equal to 0.10 and A2 may equal .08 or some other value smaller than, but as close to Al

as may be desired.

The program has at least two known practical applications. Firstly, it may be used

in the design of multiple column foundation footings where the footing is prismatic and

equal loads are applied by columns spaced at regular intervals. If the designer wishes

to minimize variations in the foundation pressure he can use the program to determine

the flexural stiffness required of the foundation. Another use for the program would be

in the design of a compression test for a wall or wall panel where it is desired to apply a uniformly distributed load either in the axial plane or in a plane parallel to

it. An approximation of a uniform load is usually achieved by using several jacks to apply concentrated loads to a load distributing beam which in turn transfers the loads

to the wall. The greater the number of jacks and the stiff er the distributing beam, the more uniform will be the wall load. Test site space restrictions and economy are practical

v/////\ P V//////.

FOUNDATION REACTION (FORCE PER UNIT LENGTH OF BEAM) = (K)(Y)

a 0 D D a D

L

Figure A.l - Beam on elastic foundation.

88
considerations which limit the EI of the beam and the number of jacks. Consequently, a decision is often made as to the maximum variation from the uniform load condition which

is to be tolerated.

The program permits a user who plans a wall test to try several combinations of

beam stiffness and number of jack loads once he has chosen a range for maximum variation

of the distributed wall load from the average value. Each trial gives the stiffness of

a wall which may be tested by the contemplated test arrangement without exceeding the

maximum load variation specified by the user. The program also permits the ratio, a, (see figure A.l) to be varied to maximize the foundation constant (wall stiffness)

calculated by the computer. The user must make an estimate of the stiffness of the

actual test wall. However, once this is made he can select the cheapest or the most

convenient of the contemplated test arrangements for which the com.puter output gives a larger foundation constant than his estimate of the axial stiffness of the test wall.

The basic theory and equations are found in the book, "Beams on Elastic Foundation,"

by M. Hetenyi [10] . The principal equations used are equation 42a on page 54 and the

unnumbered equation, 4 lines from the bottom of page 53 in Hetenyi's book. The program

contains a main routine and tw^o subroutines, designated subroutine SUB and subroutine

BUS. Table A.l contains a listing of the more important variables as used in this

appendix and their names as they appear in the computer program. The program which is

written in FORTRAN language, is listed in table A. 2. Each statement occupies one or more of the numbered lines of the listing. The line numbers will be used to reference

statements and parts of the program.

The input is supplied to the main program in groups of four cards. The first card

(see line 8) supplies the number of load-point cases, the number of wall-width cases,

the number of beam-stiffness (EI) cases, the values a, Al and A2 . The second card (see

line 16) supplies the number of load points corresponding to each load-point case. Thus, if there are 3 load-point cases, e.g., _4 placed in the first data coliimn would

correspond to 4 load points, 5_ placed in the second column corresponds to 5 load points

and 5_ placed in the third column corresponds to 6 load points . The third card (see line

18) supplies the width value for each walJ^width case. The fourth card (see line 20)

supplies the EI value for each EI case. The four data cards nay be repeated to obtain

additional sets of results as, for example, when it is desired to change Al, A2 or a . A

format statement follows each read statement so that the user can easily determine the

proper method of supplying data on punched cards.

The output (see the top section of table 6. A. 2) is preceded by six statements which

give the number of load cases, width cases, EI cases and a, Al and A2(see line 11 for

the format). Follovring these statements there are twelve columns in a full printout.

(Table 6. A. 2 was edited for the proposed test method presented in section 6 to provide

values of LOADS, WIDTH, EI and FOUKDK, which are of the most assistance to the user)

.

These are headed as follows: LOADS , WIDTH, EI, FOUNDK , DEVA, DEVL, DEVC , ABMAX, YSUBA,

YSUBL, YSUBC and YAVE . All the information and results for a complete case are print^.J.

89
TABLE A.l - A PARTIAL LIST OF VARIABLES

Variable Name

THIS MAIN SUBROUTINE SUBROUTINE

Description REPORT PROGRAM SUB BUS

NUMBER OF POINT LOADS n IPOINT(JJ), N LI L2

LENGTH OF WALL L WIDTH(KK) WIDTHS WIDTHT

FLEXURAL STIFFNESS OF

EI EI(I) EIS EIT

LOAD DISTRIBUTING BEAM

FOUNDATION

CONSTANT K FOUNDK FOUNKD KFOUND

DISTANCE BETWEEN

LOADS

D " ' D DS DT

RATIO OF EDGE

DISTANCE TO FIRST

LOAD TO DISTANCE

a

( ... , ALFA . ALAF AFLA

BETWEEN LOADS

MAGNITUDE OF A JACK LOAD

P

BEAM OR FOUNDATION

y DEFLECTION

-

BEAM DEFLECTION AT

END DIVIDED BY A YFORA YSUBA ADEFL

JACK LOAD

BEAM DEFLECTION AT

CENTER DIVIDED BY - YFORC YSUBC CDEFL

A JACK LOAD

BEAM DEFLECTION AT MOST

CENTRAL LOAD DIVIDED BY - YFORL YSUBL LDEFL

A JACK LOAD

PRESSURE DEVIATIONS FROM DEVA DIFA ADEV

AVERAGE DIVIDED BY THE AVERAGH PRESSURE - AT - DEVL DIFL LDEV

END, UNDER A CENTRAL

LOAD AND AT CENTER - DEVC DIFC CDEV

AVERAGE FOUNDATION

PRESSURE DIVIDED BY AVEY YAVE AVER

A JACK LOAD

MAXIMUM PERCENT

DEVIATION OF THE PRESSURE FROM THE ABMAX ABMXA MAXAB

AVERAGE DIVIDED

BY 100

Table A.l - A partial list of computer program variables.

90
Table A. 2 - Computer program for load distribution analy

SJ AT 4 ,L T ' MP OAT A,

^ATAi7PL7 0-5 0A/oy-i6:2<i:;^l

I . c * 2. C * 1. C *REAL LK

=>. CUMMUN X,Y,N,HOUNDK..Ai_FA,ABMAX,DEVC,LLVL,OEVA, Yf- JRA , YF U^^L . YF Q WC . 6. lAVEY.O

7. OIMFNSION I PO I NT ( 1 0 ) , I DTH( I 0 ) , E I ( J 0 ) a. 3 hJF AIJ (5 . I 0 . END=2 ) J , < , L t ALFA , A I , A2

O. 10 FUHM AT ( JI2 , 3F4. 2 > 10. WRITE(6 , 16 ) J.K.L.ALFA, Al , A2

11. 15 FORMAT ( 1 H 1 J JHNUMBFR OF LOAD CASES IS I5t/1H J3HNIJMBER OF

12. IrtlOTHS IS 15. /IH 33H^U^lghW OH BEAM STIFNESSE5 IS

13. 2 15, /IH 35hCl)C.E DISTANCE-LOAD SPACING KATIO ISF5.2./IH 2>^HUMPe-5 t< 14. 3X . LOAD VARIATION 1 SF 1 0 . 2 . /

15. <* IH 2aHLUWER MAX. LOAD VAPIATIQn ISF10,2)

16. RL AO ( 5 . 20 ) ( I POT NT( I ) . I = 1 , J

)

17. ?0 FOhiMAT (101?)

IS. Rf AD(5 ,50) (W IOTm( I ) , 1=1 ,K

)

19. SO FORMAT ( 1 0F3. 0 ) 20. HF AD (5 , 70 ) { E U I ) , I- 1 ,L ) 21. 70 ("ORyATI 1 OES. 0)

22 . *P ITE( 6,15)

2j. 15 FG.VM AT ( 1 HO 1 OHLOAO S lOHV^IOTH 9H LI IIHFOUNDK lOH

24. 1 DE VA lOH D£VL lOH OF VC lOHABMAX 10HYSU3A lOHYS

25. . 2UfiL lOHYSUBC 5H YAVE/)

26 . 00 1 IJ J= 1 ,

J

27. N=IPOINT(JJ)

28 . DC 1 ^<K= 1 ,

K

2t>. U= W I DTH( KK ) / ( FLO AT ( N- 1 ) + 2. *ALFA ) 30. X=( ALFA+FLPATC N/2-1 )) *0

Jl . Y=X +0

32. 001 3LL = 1 ,L

33. IF ( VOD ( N ,2 ) ) 51 , 51 , 52

34. 51 FC5UNOK = 200000 . 35. 7 1 CONTINUL

36. CALL SUB ( r I { LL » , 1* I DTH( KK ) ) 37. IF(AaMAX- Al)31, 32, 33

38. 31 FGUNDK=2 . *F ULNOK

39. GO TO 7 1 40. 32GuT01^

4 1. J3 HK=FOUNDK

42. FCUNDK.-F0UNDK/2

.

43. 1 7 1 CONT INUF

44. CALL SUB (E I ( LL ) , W IDTHI K <) ) 45. IF ( ABMAX-A2 )34 ,35, 36

36 FnUNDK=F0UNDK/2.

4 7, GO T 0 1 7 1 48. 35 GU TO 13

49. 34 LK^FUUNOK

50. 271 FOUNOK= (LK, + HK. )/2 . 51. CALL SUB ( El ( LL ) , W IDTH( KK )

)

52. IFtCABMAX- A2 ) . GE . 0 . . A N D . ( A BM A X- A 1 ) .L £ . 0 . ) GO T013

53. IF(A3MAX.GT. A1)HK=F0UNDK

54. IF { ASM AX .LT . A2 )LK=FOUNOK

55. Gu TO 271

S6 . 52 FOUNDK = 200000.

91
Table A. 2 cont'd. - Computer program for load distribution analysis.

37 , /2 CONTINUE

58 . CALL BUS (e I (LL ) . WI r)TH( KIC ) ) 5y • iF(AUMAX-Al )4li42>43

60 . 4 1 F(JUNDK = 2 .KUUNDK

1 , GU TO 72

f> 2 • 42 GO TO 1 3

6.T . 4 3 !-»< -FOUNDK ' ' '"^ ' 64 . FCJUNOK = FUUNOK/2 . 65 . 1 72 CONTINUE

66 • CALL RUS (E I (LL ) , * I DT H( KK ) » 67 , I'=^(AaMAX- A2)44, 45 ,46 ^. 66 « 4(3 FOUNOK=FnUNDK/2,

69. GO T U 1 7 2 , '

, 70 . 45 GO TO 1 3 , ' ' LK = FOUNOK - 7 1, 44

72, 2 72 FOUNDK= ( LK+MK )/2

73 . CALL BUS < F I ( LL ) . * I OTH( KK ) ) 74 . IF{(ABMAX- A2 ) . GE. 0 , . AND. ( ABMAX-AI ) ,LE.O . ) GO T013

75 . IF(A3MAX,GT. A1)HK=F0UNDK

76 . IF(A3MAX.LT. A2)LK=F0UN0K

77, GO TO 272

7U , 1 3 WR I TE( 6 , 91 ) IPO INT( J J ) . WIDTMi KK» ,E I ( LL ) .FOUNDK , DE V A , DE VL . OE VC

7<), 1 BMAX .YFQRAtYFOUL.rFORCf AV EV

8 0, 9 1 FORMATdH I5,F1 0 .1 , 2E10 .4, 4F 10.3,4E 10.4)

8 1, 1 2 CONTINUE ... . P2 , 1 1 CUNT INUE

83 , GO TO 3 84 , 2 STOP

P5 , END

86, c * 87 , c 68 , c 89, SUE3R0UTINE SUB < fc I S . W ID T HS ) 90 , COMMON Z, T, L 1 .FUUNKD , ALAF , AHM XA , D I F C . D I FL .01 FA.VSUBA , YSUBL, YSUBC

,

91 . 1 YAVE , DS

92 . PFAL LAMUK.LAMOL ,LAMD

93 , LAMO= ( FOUNK D/ ( 4 • £ IS ) ) *.25

94 , LAMOK=L AMD/F OUNKO

95 , LAMDL = LAML)*W lOTHS ' '

' '. XL A MO-=LA MO* 2

' 96.

97 « YLAM0=LAMO#T

98 « CLAMD=LAMD*W IOTHS/2,

^9. YSUB A=0 ,

t 10 0. YAVfc = FLO AT ( L I ) /( FOUNKO * W ID TMS)

10 1, 002 1 M= 1 , L 1

' 102, A= { ALAF +FLOAT ( M-1 ) ) *0S f

.

- 10 3, B= *l I OT HS-A •

; 104, ALAMO^LAMO*

A

105 , bLA '>^0 = LAMD*0

106. 2 1 YSUHA- YSUBA -t-LAMOK/ ( S INH( LAMOL )**2,-5lN(LAMDL)4'*2,)

10 7. 1 *2 . * ( SI (L AMDL ) * 10 8. 2C0S { AL AMD ) +0.0 SH( dL AMD ) — S 1 N ( U AMOL ) *COSH (ALAMO)*C0S(3LAMD) ) 109. I 0 = L 1 / 2 110. I 1=L 1/2+ 1 '

' • " " " ^' 111. I2=Ll/2+2

112. YLi = o, .

:

" 113. D02 2M= 10 ,L1

114. A=(ALAF+FL0AT(M-1) )*DS

92^
Table A. 2 cont'd. - Computer program for load distribution analysis.

1 1 5, fl=WlDTHS-A

116. AL AMD= LA MD*A

117. BLAMD^L AMD*P

1 1 R. 22 YL1=YL1 + LAM0K/(SINh(LAMDL) **?«— S IN(LAMDL)**2. )*<2.*C0SH( XL AMD )*cns

119. 1 {XLAMD)*(SINH(LAMOL>*COS(ALA MO ) CO SH (BLAMO)— SIN ( LAMD L) *C 03 H { ALAMO)

I ^o . 2 C OS ( ULA MO ) ) + ( COSH(XLAMO) *S IN( XLAMO ) -fS INH( XL. AMD ) *CaS ( XL AMO>)*(SINH

1 a 1 . 3(LAM0L)*SIN( ALA MO ) * CO SH ( BL AMD ) - S I NH ( LAMOL ) * COS ( ALA MO )*S INH( OLAMD) + 1?2 . 4 S I N ( L AMDL >*SINH(ALAMD)*COS{OLAMD) — SIN(LAM0L)*CUSH(ALAM())*S1N(BLAMD

12 J. 5 ) ) ) 124. YL 2= 0 . 125, IF ( I 2 . GT .L 1 ) GO TO 32

126. DO 23M = I 2 ,L1

127 . A= ( ALAF +FLOAT { M- 1 ) ) *DS

128. B-WIDTHS-A

129 . ALAMO= LAMD*A

13 0. bLAMO=LAMO*B

131 . 2 3 YL2= YL 2+-LAMOK / ( S I N H( L AMDL ) **2 . -S I N < I. AMDL )**2.)*(2.*CnSH( YLAMO )*COS

1 32 . 1 (YLAMD )*(SINH(LAMDL) COS(ALAMO)*COSH( BL AMD ) - S I N (LAMOL ) *COSH( ALAMO)

1 33 . 2*C0S( ^LA MO ) ) + (COSHCYLAMO)*S IN( YL AMD ) + S IN H( YLAMO ) *C0 S ( YL A MD ) ) * { S I NH

1 34 • 3 ( LAMOL ) *S I N ( AL AMD ) *C0S H ( BL AM 0 )— S INH(LAMOL )*COS( AL AMD ) * S I NH ( flL AMD ) 135. 4 SI N< L A MOL ) * S I NH ( ALAMO )*C DS (BLAMO )—SIN(L AMOL )*COSH( ALAMO) *S IN( dL AMD

1 36 . 5 ) ) ) 137. 32 YSUBL= YL 1+YL2

1 38 • YSC = 0 . 139. 00 24M=I 1 tLl

1 40 . A={ ALAF + FL QAT ( M — 1 ) ) * OS

141. D= W I OT HS—

A

142 . AL AMO=L AMD*A

143. hLAMO = LAMD*B

144. 24 YSC=YSC+LAMaK/(SINH(LAM0L)**2.-SlN(LAMDL)**2.)*(2.*C0SH(CLAMD)*CUS

145. 1 (CLAMD)*(SINH(LAMOL)*COS( ALAMO)* COS H(8L AM D)-SIN(LAMOL)*COSh(ALAMO>

1 46 . 2*C0S(3LAMD)>+(C0SH(CLAM0)*SIN(CLAM0)+SINH(CLAM0)*C0S{CLAM0))*(S1NH

147. 3 (LAMOL ) *S IN ( AL AMD) COSH( BLAMO)-SINH(LAMOL)*COS(ALAMO)*SlNH(aLAMO) + 14R. 4SIN(LAMDL)*SINH{ALAM0)*C0S(0LAMD)-SIN<LAM0L)*C0SH(ALAM0)*SIN(BLAM0

1 49 • 5 ) ) ) 150. YSUBC=2 . *YSC

151. 01 F A= ( YSUBA- YA VE ) / YA VE

1 52 . OIFL=(YSUBL-YAVE)/YAVE

153. OIFC=( YSUBC-YAVE )/YAVE

154. ABMXA=AMAXO(ABS(OIFA),AUS(01FL) «ABS{DIFC)

)

155. RE TURN

156. END

1 57 . C *

15fi. C

1 59 . C * 160. SUBROUTirNt BUS<E1T ,* lOTHT ) 161. COMMON Q , R ,L2. KFOUNO, AFL A , M A XA B , COE V , LDE V , A DE V , ADEF L * LOEF L C OEFL

,

162. lAVER.OT

163 . REAL L AMOK. LAMOL tLAMO.LOEFL. MAXAa, KFOUNO.LDEV

164, LAMO-( KFOUND/ (4.*tIT ) »**.25

165. LA MO K=L A MO /KFOUND

166 . LAMDL=L AMO*W I OT HT

167. CL AMO-LAMO* W 1 DT HT/2

.

168 . ADEFL=0.

169. AVER=FL0AT (L2 )/( KFOUND*'* 10 FHT ) 1 70. 00 1 1 lM-1 ,L2

171 . A=( AFLA4-FLUAT ( M- I ) ) *0T

172. B=WI DTHT-A

93
Table A. 2 cont'd. - Computer program for load distribution analysis.

173. ALAMO=LAMD*A

174. Bt AMC)=LAMO«B

175. }l\ AOFFL-AD&FL*UAMOK/(SINH(LAMOC>**2.-SIN(LAMOL)**2.

)

176. 1 2«*(S INH(LAMDL) * 177. 2<-0S ( ALAMO) *C USH ( BL AMD ) -S I N ( L AMOC ) OSH ( ALAMO) *COS ( BLAMO » ) 17a. COEFL^O . 179, lJ = (L2+.3)/2

180. IF( 1 3,FQ .2 )GO TO 1

1 bl . DO I 1 ^M=I 3 .L2

182. A-( AFLA+FLOAT( M-J I ) »DT

103. 8=WinTHT-A

164, ALA MO-LA MO*

A

185. OLAMO=LAMO*B

IPb. \\2 CDr:FL = CDtFL + 187. A LAMOK/( SI NH(LAMDL) O*? . -S I N ( LAMDL )**2, ) *(2 .COSH( CL AMD )*CaS

168 . 1 (CLAMO) (S INHCLAMOL ) *COS ( ALAMDJ »COS H( BL AMO )-S IN (LAMOL ) *C OS H( ALAMO)

189. 2*C0S ( BLAMO ) ) + {COSH( CLArtO ) SI N( CLAMO ) S I NH(CLAMD ) COS ( CL AMO ) ) * ( S INH

190. 3 ( LAMOL ) S IN ( ALAMO) COSH( BLAMO)-S INH(LAM0L ) COS( ALAMO! SINH( BLAMO)

19 1. 4SI N( LAMOL) *SI NH ( ALAMO) COS ( BLAMO )-S IN (LAMOL ) COSH( AL AM O ) ^S IN ( BL AM D 192 , 5 ) ) ) 193. 1 cje;fl=coefl*2 , 194. c jffl=coffl+lamok^ (coshc lamolj cos ( lamol »+2 .)/( 2«*<s inh (lamol ) 195. 1 si n(lamol ) ) ) 196. LDeFL=Cr)£FL

197. AOtV=( AOEFL-AVER )/AVeR

198. LOEV=( LOtFL-AVEH)/ AVER - 199. COEV-=( COEFL-AVRR ) /AVEH

200 . MAX A3= AM AXO ( Ay S ( ADC V ) , A BS( L OE V I ABS( COEV >

)

201. RETURN

20 2 . END , . , END DATA,

aURKPT PKINTJ -

9A
on a single line of output aligned under the twelve column headings. The first four

columns contain the essential information. Column 4 contains the maximum foundation

constant sought. It is dependent on the number of load points, the wall width and the

distributing beam's flexural stiffness (displayed in columns 1 through 3) plus the value

of a , Al and A2. The 5th, 6th and 7th columns of the output are quotients of the

deviations of the foundation deflections, computed at 3 locations, from the average

deflection (the uniform deflection which would occur if the load distributing beam were completely rigid), divided by the average deflection. These 3 locations are (a) at either end of the beam (DEVA) ; (b) at the load points closest to the center for even numbered load cases or at the centrally located load for odd numbered load cases (DEVL)

;

and (c) at the center of the beam (DEVC) . Columns 9, 10 and 11 give the quotients of

deflections divided by the magnitude of the concentrated loads, for the same 3 (2 for

odd numbered loads) points. Column 8 is the largest of the absolute values appearing in

columns 5 through 7 and column 12 is the average deflection divided by the magnitude of

the concentrated load. It should be noted that the values appearing in column 8 are always between the limits of Al and A2

.

It is assumed that the largest deviation of the displacement from the average

displacement - and therefore the largest deviation of the foundation pressure from the

average pressure - will occur either at an end of the beam, under a central or near

central load, or under the center of the beam. While a proof is not offered, it is

believed that the foregoing assumption is a valid one. Lines 1 through 32 of the main program (see table A. 2) are concerned with the

furnishing of data and the establishment of iterative loops for the processing of individual

sets of data. Line 33 differentiates between odd numbered loads and even numbered

loads. These cases are differentiated because odd numbered load cases require a deflection

computation at the center and at one end of the beam while even load cases require

computed deflections under one of the loads which is closest to the center, at the

center and at one end.

Lines 34 to 55 of the main program are used for even numbered load cases. An

initial foundation constant of FOUNDK = 200000 is assumed. Subroutine SUB is called

upon to give ABMAX. This is the maximum absolute value of deviation of the deflection

from the average divided by the average; it is obtained from a consideration of the

deflections at the end, under the most central loads and at the center. FOUNDK is

doubled until ABMAX is equal to or greater than the foundation constant, which is the

object of the search. Then the current value of FOUNDK is halved successively and SUB

is called each time until ABMAX is less than A2, the lower limit of the maximum variation

which has been chosen. Once an upper (HK) and a lower (LK) limit have been found for

FOUNDK, the program takes the average of these until ABMAX falls between Al and A2

.

After each unsuccessful trial a new value of HK or LK is established and the process of

finding an acceptable FOUNDK is continued. When an acceptable FOUNDK is found the

computations are transferred to the write statement on line 78.

95
Lines 56 to 77 employ the same technique except that subroutine BUS is called

during the search for an acceptable value of FOUNDK. Subroutine BUS is suitable for odd

numbers of concentrated loads. Statements on lines 81 to 83 complete the iterative

loops and allow new sets of four data cards to be accepted when it is desired to vary a, Al or A2.

Subroutines SUB and BUS use the principal of superposition, together with the

appropriate equations for the deflections. While SUB uses only equation 42a from Hetenyi'

treatise, BUS also uses a special form (lines 194 and 195) suitable for determining the

central deflection due to a central load.

The units used in the computations must be consistent. For example, it has been

found the EI in pount-inches squared, and wall width L, in inches, work well with the

initialized values of 200000 for FOUNDK used in the main program on lines 34 and 56.

The implied units of FOUNDK would then be pounds per inch of wall width per inch of

wall shortening (or foundation deflection) . Of course a (ALFA in the main program)

is unitless since it is the ratio between edge distance and the distance between loads.

The output in columns 5, 6 and 7 are deviations of the deflections from the average

divided by the average. A positive value indicates a smaller than average deflection.

One can infer from the output of these columns whether the load distributing beam is

generally bent so that the concave side is the upper or the lower. Some results have

indicated that for larger values of ALFA (above 0.5) the concave side tends to be the top

side while for lower values of ALFA the lower side tends to be the concave side. This

appears a reasonable result in view of the following considerations. The distributed

upward load on the beam can be thought of as having a large uniform value with small

superimposed perturbations. When a is large, the concentrated loads acting down are bunched closer to the center than when a is small. This causes the beam to curve so that the concave side tends to be the top side. When a is small, the concave side tends

to be the bottom side. An extreme example of the latter case would occur if a were zero

and the number of loads were 2. The distribution and amplitudes of the perturbations

are dependent on the final value of FOUNDK and the beam's flexural stiffness EI. The

influence of the perturbations on the ultimate curvature of the beam is usually negligible

however, in some instances their effects are sufficient so that the sense of the beam's

curvature cannot be predicted a priori from a consideration of the number of loads and

the value of a alone. In short, the user is warned that in some applications the shape

of the beam may differ from intuitive expectations.

96
Appendix B - Core Radius Calculations for Some Typical Wall Sections

This appendix presents example calculations that were performed using the cross sectional properties of three typical bearing wall constructions. The purpose of the exercise

was to demonstrate a method of comparing a "theoretical" core (kern) radius with the eccen- tricity of loading specified in ASTM Standard Method E72-74. The theoretical core radius

was determined on the basis of an assumption of composite behavior exhibited by the walls as

they are subjected to eccentric axial loading. The General Formulation describes the stepby-step procedure for computing the properties of the transformed section, which is formed

by using the core element as the base material.

GENERAL FORMULATION - TRANSFORMED SECTION CALCULATIONS

H =r

Neutral Axis

Inside Face'^ C

o

4

I. ASSUMING LINEAR STRAIN 5 STRESS

e = a /E , £ = a/E, z. = a./E.

0 0 0 1 1 1

II. AREA OF TRANSFORMED SECTION, A

T

e.

1 c (c -t ) (t„-c ) 0 0 o To

E c E(c -t ) E. (t„-c ) 00 00 i To

(E /E)bt ; Let X = E /E

0 \

- abt

^c

= (E./E)bt. 11; Let X. =

1 E./E ^

=

X bt + abt + X.bt.

0 0 11

'J

- b[X t + at + X.tJ

0 0 11 [1

97
TENSILE S, COMPRESSIVE STRESSES IV. LOCATION OF NEUTRAL AXIS

o A.^

r. Pec

P o

Pec

P o

O. = T— *

1 A,p

If c =0, then

o

'

'o " EA

o A^

X )5t (t /2)+atit(t +t/2)+X.tit. (t +t+t./2)

O O O O l i o 1

)f5(X ^ t^+at+X.t.)

o d 11^

D Pec

P o

Let e = r^, since P ^ 0

r =

c A^c^ [21

X t^+2att +at^+X.(2t.t +2tt.+t?)

O O O 1^ 1 O 11^

2(X t +at+X.t.)

o O 11

2 2 Assuming t , t., t t. << 1 ^ o 1 o 1

2att +at +2X.tt.

^ o 1 1 "o ~ 2(X t +at+X.t.) ^ O O 11

[3]

[4]

MOMENT OF INERTIA OF TRANSFORMED

SECTION, I„

VI . CALCULATING A^c

T o

1=- (X b)t"^ + A. (c - t /2)^

12 o o A^ o o

X bt X bt - o o

^ oo ^ ^ 2 12 4 o o

X bt (c^ - c t + 1/3 t^) [5] 0 0^0 o o ^

'

iz- abt^ + abt(t/2 + t - c )^

12 o o

1 ,^3 abt ~r T ^2

^

= _ abt * — it * 25^ -2c^)

3

=

I5- abt [t^ + 3(t > 2t^ - 2c^)^][6]

o o ~ 2 X.bt^ + A (c. - t./2)

12 1 1 c 1 1

c

= 12 \K * h^h - % - h/2v

c

= n Vhf^i^^t^vvh)']

^A ' ^ ^C

17]

[8]

A^c = ^ [X t^+2att +at^+X.(2t.t + To 2^00 o 1*^10

2tt.+t:)]

1 1' ^

A„c = ^ [X t +2att +at +X.(2t.t + To 2*^00 o I'-io

2tt.+tf)]

1 1^ [9]

98
Fir -^L/TJD^-*/ \

ti -s. O.5io t = 3. 5 <o

.Distance From Out&ide Face to Ne>jTgA<- Axis.t^g^ Eqki. L^:!

C» » 2. 04^/ l,4Si> -1-375 in.

Approximate c, EaN.L+l

Co j=f 2 Ll-ilt.i>^LO.0l^6) t 0. 0^36 j/^.itbj -t 2 uO-IZ^)L l-l^> •= 1-234 ih. t.4Si>

MoMgMT OF I»jgeT»\ pp Transformed AgeA^ Ij. - — Eoms. L & J^C^X Lll 4 1 83

c C|.37W^= I. S*?©* >obto= a^373Uto;t<^.37^y ~ 5, <p23

C-tc « (./.37SJ C3.i7i>> = 5.5f&i. X t> tt /7Z - O. JZ5 i lio ji'^.i,} //Z =. 0.083^

Ia = 5.*25 n-B^Ote - O.SISfc + '/^ / O.J4> = 5.fr23 L 1-422)- 7-<^<ih Ib= ^J-^SS r/Z.2b + 3 5 + 2 X 0.373- 2.75)^ J s 3-^22

Ic^ O.0B'6^L 0.2b + 2>(e.lb-2-1b - 0.25)^ ^ = A.2&2>

Lj^ Ia + Ift + lo

e. Tt'ti' t 9.322 f e.2S6^ 24-»0 in.*

Eccentricity to MAk.e <y«>-^j Eqns.L2J < 1.^1

rL» It / At Co

Arco ^^<. 2.042.; r/b. 3a<c>

99
Caucjlatco from ABove -

- C Co + rtj =• 4. 37d - t/.37& + /.si> = Z.-*^ c i>»*r. f/com /A/<,rfie ^.*cff;

Fff.oM Sect. 7 OF A&tM B72-

t^/^ » 4 j>Tb/3,?i 4koiu I Dis»T. From Imside Face J

100
Yi CE LLOTEX

b- 24 If4 to- O. 'sin 0.1 XlO^pii

BO^cIO" pit

to = 0.25

CalwJuAtiom of M^viEMT OP lKiE;tT)A OF Zfe Section

"t « 3. -35>l (N.

1.125

= 3.52i(. -5-051;- a/7*^«?

A ^ -= 1. 12=> (.'^35>'-'

- £i£&2±

2A « i?-3l35 iN^

A(2)>'v^ a 0./7?toC3-&23/£ + s?. 35^; = 0.5/55

Moment of Inertia

I si)* V/i ..00»lKi.525/ + C.;7^fcti.8;i-/70a7r

L^* O. 2«t.O

£1 s O.SSi^ iw^

X A>f 0,5 /N^

9. Z -a 0.5 341 - /,703 7/V (.PuaMToP^

0.? 1^5

101
UlSTAhJCB FfiOM OuTSioe /v>wE To Tub Nbjt^Al Ai^t^.c^

Ab . O. 35/ ( /.5 + I. IHb -t 3.522>) = 0.3I35

At - i! Co = 0.03iic3.j!5j i- 0-3l3bCo.f> t I.tl2b) + O.07^Bt. -tS.^ii -f Q.^Stj

, 0.4 332

'

Co m Q.OIO t 0. 7i4 f D.34-f _ ^.S02//^

0.4332

C0t„= y-Sy^ Xcbtj = O.QOiBb C 24k OSJ a O. OO^im

2Co* 2Li.502J - S.OO f2 ^2

Ia= O.isili + 0.3J3S C 2.50 - (A 7037 tO.SJJ*^ 0.<x>OfB

Ifc I. Of24 iH*

£CCB^Tt<l s^lT't TO M^t^B gja Oj C '

rc» l-^f24 -a 0.4mi2.S02j .,' i

Comparison of n. <V»rw ScceNTKiciri /a Jj?-/-^;?^ / 3^ A^TM £74^

tjj^= 4.^25/j •= J.^4i

PeRCEWT DiFF£R£UC£^ /54i-/.t/5 - 38;^

MIS

102
-n-Tf J i I l-TT

I

I ? In

= 1.5 IM L - l<e IN

Moment op Ikc/^t/a :>f TzAssFon^^Bti AagA^ 1^

E e MTK.I ^1 TY r*' MAcE ? J Tu

tf - (. r^, ^ = 4-. S - 3. o 86 -r /. 4-12 itJ

PeeCEMT P/FFER£»JC£ =. I, 5- ;.4/2 - 67.

1.412

103
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. IHJIU. [CATION OR Rl-;PORT NO. NBSIR 75-779

2. Gov't Accession

No.

3. Recipient's Accession No.

4. T1TL[-: AND SUBTITLL;

The Development of an Improved Compression Test Method for

Wall Panels

5. Publication Date February 1976

6. Performing Organization Code

461.01

7. AUTHOR(S)

C.W.C. Yancey and L.E. Cattaneo

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

lU. Proiect/ 1 ask/ work Unit No. 4618491

11. Contract/Grant No. IAA-H-37-72 Task 130

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Office of Policy Development and Research

U.S. Department of Housing and Urban Development

Washington, D.C. 20410

itjt lype oi i\eporL ot r eriou Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) , . , , , . , An experimental and analytical investigation of the primary factors involved m the testing

of prototype wall panels under axial compression loading is reported. The objective of

the investigation was to develop a method of testing wall specimens that incorporates the

best features of ASTM Standard Method E72 while at the same time incorporating improvements in the areas of deficiency in the Standard. Twenty-five laboratory tests were

conducted on samples composed of five types of wall panel construction. The panels were

tested to failure under either of two different eccentricities of load, while being supported with one of two types of idealized end conditions. Selected test results and detailec

descriptions of the laboratory procedures used are presented. A computer-aided analyticc

study of the variables affecting the degree of uniformity of loading was conducted. Equctions based on the analogy of beams supported on elastic foundations were used in the

analysis. A study of the statistical parameters commonly used to interpret test results was conducted to establish useful guidelines for predicting structural performance on

the basis of small sample test results. A compression test method applicable to traditional and innovative wall constructions is presented. The principal additions in the revised

test method are as follows: (a) a provision for variable eccentricity, (b) a procedure

for selecting a load distribution assembly which will be compatible with the test panel,

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Compression; eccentric loading; flat-end; kern; loading rate; pin-end; test method;

wall panels; walls.

18. AVAILABILITY jy^xUnlimited 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

1

' For Official Distribution. Do Not Release to NTIS

UNCL ASSIFIED 107

1

' Order From Sup. of Doc, U.S. Government Printing

Washington. D.C. 20402. SD Cat. No. Cn

Office 20. SECURITY CLASS

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22. Price

Ix 1 Order From National Technical Information Service

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