Implementation of Compressible

Shoring Analysis for Multistory

Concrete Construction

John L. Gross

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Structures Division

Gaithersburg, Maryland 20899

December 1984

Of

NBSIR 84-2964

IMPLEMENTATION OF COMPRESSIBLE

SHORING ANALYSIS FOR MULTISTORY

CONCRETE CONSTRUCTION

NATIONAL BUREAU OF STANDARDS

LIBRARY

no.

John L. Gross

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Structures Division

Gaithersburg, Maryland 20899

December 1984

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

ABSTRACT

This report presents an analytical procedure for determining the

loads on the shoring system and supporting slabs in multistory

cast-in-place concrete construction. The procedure assumes that

the slabs are supported by evenly distributed compressible shores

and reshores and employs the stiffness method of analysis to

solve for the loads on the shoring system and slabs as construction advances. The number of shores and reshores? shore, reshore

and base support stiffnesses? casting rate? and concrete strength

gaining characteristics are considered in the analysis. Details

of the implementation of the shoring analysis in the form of a

computer program are presented. The strategy for determining the

next phase in the casting cycle is described and the details are

given for formulating the stiffness equations and loads for each

phase. Several example problems are presented to demonstrate the

use of such a procedure in assisting to make critical decisions

regarding planning of the casting schedule and determining when

formwork can be safely removed.

KEY WORDS: Buildings? Computer models? Concrete construction?

Concrete (reinforced)? Formwork? Safety? Structural analysis

i
TABLE OF CONTENTS Page

ABSTRACT. . i

LIST OF FIGURES iv

1. INTRODUCTION 1

1.1 BACKGROUND 2

1.2 SCOPE OF REPORT 3

2. MULTISTORY CAST-IN-PLACE CONCRETE CONSTRUCTION 5

2.1 CONSTRUCTION PHASES 5

2.2 COMPRESSIBLE SHORING SYSTEM 7

3. COMPRESSIBLE SHORING ANALYSIS 11

3.1 STRUCTURE IDEALIZATION 11

3.2 STIFFNESS ANALYSIS 12

4. IMPLEMENTATION OF SHORING ANALYSIS 16

4.1 DETERMINING CONSTRUCTION PHASE 16

4.2 STIFFNESS EQUATION FORMULATION 19

4.2.1 Phase 1 - Casting of the Next Floor 20

4.2.2 Phase 2 - Removal of the Lowest Reshores... 21

4.2.3 Phase 3 - Removal of the Lowest Shores 22

4.2.4 Phase 4 - Reshoring of the Vacated Story... 23

4.3 LOADING CONDITIONS 24

4.4 SLAB AND SHORE LOAD CALCULATION 26

5. EXAMPLE PROBLEMS 42

5.1 COMPARISON OF RIGID AND COMPRESSIBLE SHORES 43

5.2 COMPARISON OF SHORING SCHEMES 43

5.3 COMPARISON OF PRECOMPRESSION RATIOS 44

6. SUMMARY 51

ii
TABLE OP CONTENTS (Continued) Page

7. REFERENCES 52

APPENDIX A - Notation 53

iii
LIST OF FIGURES Page

Figure 2.1 - Phase 1: Install Forms and Shores and Cast the

Fifth Floor 9

Figure 2.2 - Phase 2: Remove Reshores from the First Story.. 9

Figure 2.3 - Phase 3: Remove Shores from the Fourth Story... 10

Figure 2.4 - Phase 4: Reshore the Fourth Story with Precompression 10

Figure 3.1 - Structure Idealization 15

Figure 4.1 - Flowchart for Determining Next Phase 28

Figure 4.2 - Phase 1 Configurations 30

Figure 4.3 - Flowchart for Phase 1 31

Figure 4.4 - Phase 2 Configurations 32

Figure 4.5 - Flowchart for Phase 2 33

Figure 4.6 - Flowchart for phase 3 34

Figure 4.7 - Phase 3a Configuration 35

Figure 4.8 - Flowchart for Phase 3a 35

Figure 4.9 - Phase 3b Configurations 36

Figure 4.10 - Flowchart for Phase 3b 37

Figure 4.11 - Flowchart for Phase 4 38

Figure 4.12 - Phase 4a Configuration 39

Figure 4.13 - Flowchart for Phase 4a 39

Figure 4.14 - Phase 4b Configurations 40

Figure 4.15 - Flowchart for Phase 4b 41

Figure 5.1 - Eight Story Building 45

Figure 5.2 - Plot of Slab Load Ratio vs. Age of Slab 46

Figure 5.3 - Comparison of Rigid and Compressible Shores.... 47

Figure 5.4 - Comparison of Shoring Schemes 48

Figure 5.5 - Comparison of Precompression Ratios

(0% and 50% precompression) 49

Figure 5.6 - Comparison of Precompression Ratios

(50% and 100% precompression) 50

iv
1 . INTRODUCTION

In cast-in-place concrete building construction, each

freshly cast floor is supported by a system of shores and reshores which transfer the weight of the concrete, workers and

equipment to the floors below. If the shoring system is not

designed with sufficient strength and stability to carry the

imposed loads, a collapse of the shoring system and, possibly the

structure it supports, will result. Additionally, construction

loads on the supporting slabs, imposed by the shoring system, may

be greater than the service loads for which the slabs were

designed. Since the supporting slabs have generally not reached

their full design strength, their capacity may be exceeded

resulting in failure.

In the course of casting a multistory concrete building,

formwork is removed and shores and reshores are relocated as

construction progresses. As a consequence, the structural load

carrying system is constantly changing, making it difficult to

assess the distribution of loads on the structure or shoring

system at any given time. Decisions regarding the removal of

forms and relocation of shores are often made without the benefit

of an analysis. Premature removal of shores which lead to a punching shear failure in the slab was cited as a probable cause

of the collapse of the Skyline Plaza apartment building in

Fairfax, Virginia, in 1973 (1).

- 1 -
This report presents an analytical method which has been

developed for determining the loads on the shoring system and

supporting slabs as construction advances. The theory behind the

method and comparisons with other analytical models and with

field test data are covered in a separate report 1

. The procedure assumes that the slabs are supported by evenly distributed

compressible shores or reshores. Forces on the slabs are computed by assuming that superimposed construction loads are distributed to the shoring system and interconnected floors in

proportion to the relative stiffnesses of the slabs, shores,

reshores and ground. This report focuses on the implementation

of such an analysis for solution by computer.

1 . 1 BACKGROUND

The contractor is guided in the design of formwork by

American Concrete Institute (ACI) Standard 347, Recommended

Practice for Concrete Formwork (2). In the section addressing

multistory structures, ACI Standard 347 states,

"...No shoring should be removed until the concrete has

gained sufficient strength to support the loads which

will be transferred to the structure upon removal of

such shoring."

While no procedure is specified for determining the loads that

will be transferred to the structure. Formwork for Concrete (3),

sponsored by ACI Committee 347, describes a procedure for analyz1 Fattal, S. G., Gross, J. L. , and DeLorme, A. J., "An

Analytical Model for the Design of Shoring Systems Used in

Concrete Building Construction," NBS Building Science Series

Report, in progress.

- 2 -
ing the shoring loads in multistory structures. This method,

based on the work by Grundy and Kabaila (4), assumes that the

shores are infinitely stiff relative to the slabs. Grundy and

Kabaila point out, however, that wooden shores have sufficient

compressibility to significantly modify the distribution of loads

among the interconnected slabs. Including the compressibility of

the shoring system tends to shift the slab loads to the uppermost

interconnected floors as compared with an analysis assuming rigid

shores. A complete finite element analysis, including compressible shores, for the investigation of the construction collapse

of the Harbour Cay Condominium in Cocoa Beach, Florida (5)

confirmed this effect.

The development of a simplified analytical procedure which

accounts for the stiffness of shores and reshores was undertaken

by the National Bureau of Standards (NBS), A computer program

was developed, based on the stiffness method of analysis, which

includes variable shore and reshore stiffness, nonrigid base

support, and installation of reshores with precompression. This

report describes, by means of logic flowcharts, the implementation of this analytical procedure on either a mainframe or desktop computer. The purpose is to make available to others a model

on which to build and expand the concepts described herein.

1.2 SCOPE OF REPORT

Section 2 describes the sequence of steps (phases) in forming and shoring a typical floor of a multistory concrete building. The four phases of a casting cycle for each floor describe

the structural configurations and loadings which must be considered in an analysis. In section 3, a model is presented for

idealizing the structure and the fundamentals of a stiffness

analysis of the interconnected floors are described. The details

for implementing the stiffness analysis are given in Section 4.

Here, the overall strategy, or program flow, is described and

- 3 -
details are given for formulating the stiffness equations for

each phase of casting. In addition, the formation of the loading

condition for each phase is presented and the calculation of slab

and shore forces is outlined. In Section 5, several example

problems are solved to illustrate the application of such an

analytical procedure to assist in making critical decisions regarding planning of the casting schedule and determining when

formwork can be safely removed.

- 4 -
2. MULTISTORY CAST-IN-PLACE CONCRETE CONSTRUCTION

In multistory cast-in-place concrete construction, each

freshly cast floor slab is supported by a system of shores and

reshores which transfer the loads to the previously cast slabs

below. The loads are distributed to the interconnected slabs in

proportion to the relative stiffness of the slabs and the formwork system. This section describes the sequence of steps in

forming and shoring each floor of a multistory concrete building

and discusses the importance of accounting for the compressibility of the shoring system in an analysis.

2.1 CONSTRUCTION PHASES

A typical casting cycle for a scheme which uses both shores

and reshores consists of the following four phases:

1) Install a story of shores and forms and cast the floor

slab above

2) Remove the reshores from the lowest reshored story

3) Remove the forms and shores from the lowest shored

story

4) Place reshores in the story in which the forms and

shores were removed

It should be noted that ACI Standard 347 (2) suggests that

reshores should be installed "snugly" under the slab just

stripped so that the reshores are relatively load free upon

installation. If deflection is to be controlled, however, the

reshores may be installed with a precompression such that the

total load due to precompression approaches that on the shores

prior to their removal. The precompression of reshores is

accounted for in the analysis described here by specifying a "precompression ratio", P, where 0 < P < 1. The load in the

reshores upon installation is computed as the load in the shores

-5 -
prior to their removal times this precompression ratio. By using

a value of P equal to zero in the analysis, the installed reshores will be load free.

The four phases of a casting cycle noted above may be illustrated using the multistory building shown in Figures 2.1 through

2.4 . In these illustrations the fifth floor slab of a multistory building is cast and the formwork is advanced in preparation for casting the sixth floor. The floors are numbered from

the bottom of the building to the top, beginning with the first

floor above ground level. A story has the same number as the

floor slab above it (e.g., the reshores in the third story support the third floor slab). The structure has two levels of

shores (denoted by XX) and three levels of reshores (denoted by

I |). The lowest level of reshores is grounded (or supported at

ground level).

Figure 2.1 shows the configuration when the fifth floor is

being cast (Phase 1), The weight of the fresh concrete is distributed to the interconnected floors and the foundation through

the formwork system. The stiffness of the floor slab is taken to

be zero since the concrete has no strength initially.

Phase 2, removal of the reshores from the first story, is

shown in Figure 2.2. The removal of the first story reshores is

equivalent to applying a load to the first floor slab, in a

downward direction, which is equal to the compressive load in the

reshores prior to their removal. Thus, the load applied to the

lowest interconnected floor slab is that load acting on the reshores at the end of Phase 1. In this particular example, the

load previously carried by reshores in the first story, is distributed to the remaining five interconnected floor slabs.

In Figure 2.3, the shores in the fourth story are removed

(Phase 3). The load in the shores prior to their removal is

applied to the two interconnected floors above the vacated story

- 6 -
and the three interconnected floors below it. The direction of

the load is down on the slab above the vacated story (removal of

support) and up on the slab below the vacated story (removal of

load). In general, two separate stiffness analyses are required

for Phase 3.

Finally, Phase 4 is illustrated in Figure 2.4. Here the

fourth story is reshored with a precompression load equal to the

load in the shores prior to their removal in Phase 3 times the

specified precompression ratio. As in Phase 3, two separate

analyses are required to determine construction loads on the

interconnected floors above and below the reshored story.

2.2 COMPRESSIBLE SHORING SYSTEM

The ACI 347 Standard tacitly endorses a shoring analysis

which assumes both rigid shores and reshores and rigid base

support (see Reference 2). The implications of these assumptions

need to be clarified. If a rigid shoring system is used, the

loads are distributed to the interconnected floors in proportion

to the relative slab stiffnesses. ACI (Reference 2) recommends

that all slabs have the same stiffness; that is, no account is

taken of the lower stiffness of early-age concrete. If the

system of shores and reshores is compressible rather than rigid,

a greater portion of the loads resulting from casting a new floor

will be distributed to the uppermost interconnected floors.

These floors, being the most recently cast, may not have gained

sufficient strength to carry the loads without distress or possible failure. It is, therefore, important to account for the

effects of compressible shoring and reshoring on the distribution

of construction loads in multistory cast-in-place concrete construction.

The flexural stiffness of an uncracked section may be taken

to be directly proportional to the modulus of elasticity of

- 7 -
concrete, E c , which increases with age. Since the age of the

concrete differs throughout the structure, a more realistic

approach would be to distribute the loads between the slabs in

proportion to their flexural stiffnesses based on E

c

. With a

variable modulus approach the lower floors, being older and

therefore stiffer, carry a greater proportion of the load than

would result from a constant modulus approach.

It should be noted that assuming a constant E

c and rigid

shoring system does not produce the same effect as using a variable E

c and including the compressibility of the shoring system.

Several points supporting this argument follow. First, the

modulus of elasticity of concrete increases rather rapidly as

compared with compressive strength and including the effects of a

variable E

c does not significantly modify the load distribution

except for very short casting cycles (4). Secondly, the construction loads which a slab experiences may be in excess of service

loads, and since a slab will likely be cracked under such loads,

the proportionality of flexural stiffness with respect to E

c

is

doubtful. Blakey and Beresford (6) have reported that the flexural stiffness of a cracked reinforced concrete section is mainly

dependent on the percentage of reinforcement and not on E

c

. It

could, therefore, be concluded that slab stiffnesses are in fact

relatively independent of the concrete modulus and that the

assumption of a constant modulus cannot be counted on to offset

the effects of compressible shoring.

An exact analysis of a multistory concrete building, with

material properties that vary throughout the structure and with

an elaborate system of discrete shores and reshores, each with an

unknown preload, is a formidable task. Certain simplifications

must be introduced to render the problem tractable. The simplified procedure described herein provides a working framework for

expansion to more precise analyses.

- 8 -
XX

5

A

XX XX

•tO

II o

p

2nd story — II

Cm

1

II w

XX denotes shores

II denotes reshores

denotes uniform

floor loading

Figure 2.1 - Phase Is Install Forms and Shores and Cast the

Fifth Floor

5

A

XX

4

r* XX

o

p

II C.

1

II Hi II

Figure 2.2 - Phase 2: Remove Reshores from the First Story

- 9 -
Figure 2.3 - Phase 3: Remove Shores from the Fourth Story

Figure 2.4 - Phase 4: Reshore the Fourth Story with

Precompression

- 10 -
3. COMPRESSIBLE SHORING ANALYSIS

This section describes a model for representing the dominant

effects of a compressible shoring system while maintaining simplicity. To determine the load distribution, a stiffness analysis is employed which accounts for the slab stiffness at earlyage, the stiffness of the ground which supports the first level

of shores, and the stiffness of the shores and reshores. (The

term "ground" is used here to mean "ground support system" which

could be the soil or a slab on-grade.) The structure idealization is described first and then the details of the analysis

including formulation of the stiffness equations are presented.

3.1 STRUCTURE IDEALIZATION

For analysis purposes, a multistory concrete structure under

construction may be modeled as described below. The columns of

the building are assumed to be axially and flexurally rigid. In

addition, slab continuity between adjacent bays is ignored.

These two assumptions reduces a multibay building to a series of

single bay structures as shown in Figures 2.1 through 2.4. Each

of the interconnected floors (floors connected by either shores

or reshores) in the structure is represented by a single displacement degree of freedom, u^. The stiffness of a given floor,

k n

, is computed from the geometry of the slab and the elastic

modulus of the early-age concrete if desired. The slab geometry

comprises span length in two directions, slab thickness, and

boundary conditions which reflect the edge fixities at adjacent

bays or at the building perimeter. The stiffnesses of the

shores, reshores, and ground are input to the analysis and may be

different for each bay in the structure. Shores and reshores are

assumed to be uniformly distributed and their stiffnesses, as

well as the ground stiffness, are expressed in terms of load per

unit area / unit deflection (e.g., psf/ft). A new loading condition is introduced to the system of interconnected floors when

- 11 -
a floor is cast (Phase 1). The remaining operations (Phase 2

through Phase 4) produce a redistribution of forces within the

system. Depending on the construction phase, the load applied to

the structural model is the weight of the fresh concrete, the

load carried by the level of shores or reshores to be removed, or

the precompression in the installed reshores.

A schematic representation of the five story, single bay

structure illustrated previously and the associated analytical

model for Phase 1 of the construction cycle, are shown in Figures

3.1a and 3.1b, respectively. The floor slab stiffness is given

by k n where n is the floor number (numbered from bottom to top).

Each floor slab may have a different stiffness due to its thickness or the strength gaining characteristics of concrete with

time and temperature. The stiffness of the shores, reshores, and

ground are given by k s

, k

r

, and kg, respectively. The loading

for the configuration shown in Figure 3.1b represents the

weight/unit area of the fresh concrete on the top floor.

3.2 STIFFNESS ANALYSIS

In general, one stiffness equation is written for each of

the interconnected floors. The terms making up each stiffness

equation depend on the combination of shores and reshores which

support, or are supported by, the slab in question. If the

shoring system is supported at ground level, an additional

equation is included to account for the stiffness of the ground

level support and the shores or reshores in the first story. The

stiffness equations are numbered from the top of the interconnected floors down and are indicated by i, i = 1 to Q, where Q is

equal to the number of interconnected floors. Each floor is

directly connected, by either shores or reshores, to the floors

immediately above it and below it. Thus, the i-th stiffness

equation will, in general, have terms multiplying displacements

u

i — i

, u^, and u^ + i* The concentrated force/unit area

- 12 -
corresponding to the i-th equation is denoted by w^.

A total of nine different configurations (cases) can be

identified depending on the combination of shores and/or reshores

which contribute to the stiffness of the particular floor or

ground level. For example, a floor which supports a level of

shores and which is itself supported by a level of reshores is

identified here as Case 4. The nine cases and their associated

stiffness equations are as follows:

Case 1 - Slab and shores in story below:

< k

s + kn> ui " k s

u i+l = w i (3-D

Case 2 - Slab and reshores in story below:

(k

r + kn

) u

L - kr u i+1 = vt i (3.2)

Case 3 - Slab and shores in stories above and below:

" k s u i-l + ^k

s + k n^ u

i ” k

s u i+l = wi (3.3)

Case 4 - Slab, shores in story above, and reshores in story

below:

- k

s u i-l + ( k

s

k

r + k n^ u

i — k

r u i+l = w i (3.4)

Case 5 - Slab and reshores in stories above and below:

-k r u i-l + < 2k r + k n> u

i ~ k

r u i+l = wi (3.5)

Case 6 - Slab and shores in story above:

~ k

s u i-l + ^ k

s + k n

} u

i = w i (3.6)

- 13 -
Case 7 - Slab and reshores in story above:

(3.7)

Case 8 - Ground and shores in story above

(3.8)

Case 9 - Ground and reshores in story above:

“k

r u i-l + ( kr + k g) ui = wi (3.9)

The relationship between the stiffness equation number, i, and

the floor number, n, depends on the particular phase of the

construction cycle and is defined in the next section. In addition, the specific form of the load vector, w^, is given in

Section 4.4 for each of the four phases.

- 14 -
a) Structure

representation

b) Analytical

model

Figure 3.1 - Structure Idealization

- 15 -
4.0 IMPLEMENTATION OF SHORING ANALYSIS

This section, which discusses in detail the implementation

of a compressible shoring analysis, is divided into several

parts. First, a description of the overall flow of the program

is presented. Here the logic is given for determining the next

applicable phase of a casting cycle. Next, the details are given

for computing the structural stiffness equations for the interconnected floors for each of the four construction phases. Then,

the loading for each phase is covered. Finally, the computation

of slab and shoring system forces from the known displacements is

described.

4.1 DETERMINING CONSTRUCTION PHASE

The approach taken here to solve the problem of determining

construction loads at all stages in the forming and shoring

process for multistory cast-in-place construction, may be

described as follows. Essentially, the analysis program "builds"

the structure beginning with casting of the first floor and

ending with casting of the top floor or roof. After each floor

is cast, that is the load of the fresh concrete is distributed to

the interconnected floors and shoring system, the program

determines the next construction phase to be completed. The

shores or reshores are removed or installed as applicable and a

new distribution of forces within the structure is computed.

This process is repeated until all four construction phases, as

applicable, have been executed. The program then advances the

shoring to the next floor level and applies the load of the fresh

concrete. The above procedure is repeated until all of the

floors have been cast. The loads resulting from the completion

of any phase are added to those already existing on the structure

and shoring system. Results are reported after each phase is

completed and include the current structural configuration and

updated loads on the floor slabs and shoring system.

- 16 -
The structure and shoring scheme are defined by the total

number of stories in the completed structure, N t

, the number of

shored stories, N s

, and number of reshored stories, N r

. Note

that N

g

and N

r describe the maximum number of shored and reshored

stories and not the number of shored or reshored stories at any

given time; thus, N

g

and N

r do not change. N is used to indicate

any floor level, while the floor most recently cast is designated

by N

c

(N c

= 1 to N t

). Two additional variables are necessary to

define the configuration of the constructed building at any given

time; the lowest shored story, Ls

, and lowest reshored story, L r

. For example, consider the structural configuration shown in

Figure 2.3 which illustrates the removal of the lowest level of

shores, those in the fourth story, after casting the fifth floor.

After completion of this phase, the structural configuration is

defined by N c = 5, L

g = 5, and L r = 2.

A flowchart for determining the next phase of construction,

in terms of the variables introduced above, is shown in Figure

4.1. The flowchart symbols conform to ANSI Standard X3.5 [7].

Within a decision symbol, the two quantities to be compared are

separated by a colon (:). Alternative paths are indicated by

labeled flowlines. For example, the first decision block in

Figure 4.1 compares the variable L

s with zero (L g

:0). The logic

of the program requires two alternative paths; one for n L

g equals

zero", and the other for "L

g

is not equal to zero". The two

paths are indicated by flowlines labeled = and /, respectively.

The direction of flow is indicated by arrowheads on all flowlines

for clarity. The striped process symbols (those for Phase 1

through Phase 4) indicate that a more detailed representation is

to be found in flowcharts to follow. In the more detailed flowcharts, an identification number is placed in the upper right

corner of some of the symbols and is used for reference in the

text. The flowchart in Figure 4.1 is straight-forward and no

reference to specific blocks is required. A detailed description

of its logic follows.

- 17 -
Phase 1 consists of installing the formwork and shoring for

the next floor slab to be cast and then placing the concrete. In

this step, the load of the freshly placed concrete is distributed

to the interconnected floors through the formwork system. This

phase is the first phase of each casting cycle and is always

carried out. Before the first floor is cast the counter for the

lowest shored story is set equal to one (Lg=l). This counter is

then incremented each time the lowest level of shores is removed

(see Phase 3). If the top floor of the building is cast (Nc=Nt

),

the program terminates.

Phase 2 consists of removing the reshores from the lowest

reshored level. This step is omitted if there are no reshores in

the structure (N

r -0), or if all the reshores are not yet in place

(NC <NS+Nr

). Otherwise, the lowest level of reshores is removed

and the load carried by the reshores prior to their removal is

distributed to the interconnected slabs. At the completion of

this step, the counter for the lowest level of reshores is incremented by one (L

r =L r +l).

Phase 3 consists of removing the lowest level of shores. It

is carried out only if all shores are in place (N c >N

g

). The

loading consists of the shore force prior to removal. This load

is distributed to the interconnected floors in proportion to the

relative stiffnesses of slabs, shores and reshores. When Phase 3

is completed, the counter for the lowest level of shores is

incremented by one (L g

=L

g+l).

Phase 4 consists of installing reshores in the story which

was vacated by the removal of shores (Phase 3). It will be

executed provided that reshoring is specified (N

r >0). This step

will have no structural consequence if the precompression is zero

except for the addition of the reshores as structural elements

for subsequent calculations. If, however, the precompression is

greater than zero, a force distribution will result from this

step. When this phase is executed for the first time (L

r =0), the

- 18 -
counter for the lowest reshored level is set equal to one

(L

r =l). This counter is incremented when the lowest level of

reshores is removed (see Phase 2).

It should be noted that the values of the counters for the

lowest shored level (L g

) and lowest reshored level (L

r

) may not

always reflect the true conditions prior to the completion of a casting cycle. For example, if there is only one reshored story

(level n) and that level of reshores is removed in Phase 2, the

counter will indicate that the lowest reshored story is n+1.

This will not be correct until the vacated story is reshored in

Phase 4. At the completion of any casting cycle, however, the

counters will reflect the actual configuration.

4.2 STIFFNESS EQUATION FORMULATION

Once it has been established which phase in a casting cycle

is to be executed, the forces in the slab and shoring system for

that phase are computed. This is accomplished by forming the

structural stiffness equations for the interconnected floors in

terms of the unknown floor displacements, and by solving for the

unknown displacements and back-substituting to find the forces.

In this section, the logic is presented for forming the stiffness

equations for each of the four phases by reference to the nine

cases defined in Section 3. In addition, the special cases in

which the slab and formwork forces are determined directly from

equilibrium are identified. The solution of the stiffness equations for the displacement degrees of freedom is straight-forward

and is not covered here. The formation of the loads for each

phase is covered in Section 4.3 followed by a discussion of the

computation of slab and shoring forces in Section 4.4.

For Phases 1 and 2, there is no interruption in support

provided by shores and reshores from the top floor to the lowest

level of shoring (refer to Figures 2.1 and 2.2) and, consequent-

- 19 -
ly, there is only one set of equations to solve. However, for

Phase 3, depending on the combination of shores and reshores, two

sets of equations may be required. One corresponds to the interconnected floors above the story where the shores are being

removed, and the other to the floors below (refer to Figure 2.3).

Likewise, Phase 4 may require solution for the levels above and

below the reshored story (refer to figure 2.4).

4.2.1 Phase 1 - Casting of the Next Floor

Eight of the nine cases defined in Section 3 are applicable

to Phase 1. Selection of the appropriate case depends on the

combination of shores and/or reshores which connect to the particular floor or ground level. To illustrate all eight cases,

four separate configurations must be considered: 1) shores are

grounded, 2) shores are not grounded and there are no reshores,

3) reshores are grounded, and 4) reshores are not grounded.

These four configurations are shown in Figures 4.2a through 4. 2d.

In addition, the eight cases (Case 1 and Cases 3 through 9) are

indicated next to the corresponding floor or ground level. For

example, Case 6 (see Figure 4.2b) refers to the situation where

the lowest interconnected slab supports a level of shores. Selection of Cases 6, 7, 8, or 9 depends on the determination of

which of the above four configurations is applicable.

To form the stiffness equations for the interconnected

floors, the following steps must be performed:

1) Compute the number of equations (interconnected floors)

2) For each equation, select the appropriate case based on

the configuration

3) Compute the floor number for determining the slab

stiffness

The flowchart for forming the stiffness equations for Phase 1 is

shown in Figure 4.3.

- 20 -
In Blocks l.A through l.C, the number of stiffness

equations, Q, is computed. Block l.D begins a "do loop" which is

performed for each equation. Within this loop, the stiffness

equations are formed by branching to the applicable case. To

compute the stiffness of a particular slab the floor number must

be known. The calculation of the floor number in terms of the

equation number is given in Block l.E. The remaining decision

blocks determine which of the eight cases is applicable. Blocks

l.F and l.G determine if the floor in question is the top floor

(i=l), the lowest interconnected floor or ground (i=Q), or an

intermediate floor (Ki<Q). Case 1 applies for the top floor.

Block l.H determines, for an intermediate floor, whether there

are shores or reshores in the stories above and below it (Cases

3, 4, or 5). Block 1.1 determines whether the shoring system is

grounded or not. If not. Block l.J determines whether there are

shores or reshores supported by the lowest floor (Cases 6 and 7,

respectively). If the shoring system is grounded. Block l.K

determines whether the first story contains shores or reshores

(Case 8 or Case 9)

.

4.2.2 Phase 2 - Removal of the Lowest Reshores

Six different cases apply to Phase 2. Two separate configurations must be considered to illustrate all six: 1) there is

more than one level of reshores, and 2) there is a single level

of reshores. (Recall that Phase 2 will be skipped if there are

no reshores or if not all the reshores are in place.) These two

configurations are shown in Figures 4.4a and 4.4b. As before,

the six cases (Case 1 and Cases 3 through 7) are indicated next

to the corresponding floor. The steps in forming the stiffness

equations are similar to those described for Phase 1. A flowchart for Phase 2 is shown in Figure 4.5.

In Block 2.A, the number of stiffness equations is computed.

Block 2.B begins the do loop on the number of equations. Again,

- 21 -
the stiffness equations are formed within this loop by branching

to the applicable case. The calculation of the floor number is

shown in Block 2.C. Blocks 2.D and 2.E determine if the floor in

question is the top, intermediate, or lowest floor. Case 1 is

selected if it is the top floor. Block 2.F determines the combination of shores or reshores which support or are supported by

the intermediate floor (Cases 3, 4, or 5). Block 2.G establishes

whether there are one or more levels of reshores. If there is a

single level, Case 6 is selected? if more than one, Case 7

applies.

4.2.3 Phase 3 - Removal of the Lowest Shores

Phase 3 is slightly more involved than either Phase 1 or

Phase 2. First, it involves, in most cases, two separate solutions. Determination of slab and shore loads above the story in

which the shores are removed is designated Phase 3a. The calculation of slab and reshore loads below the vacated story is termed

Phase 3b. Depending on the shoring scheme, a stiffness analysis

may not be required. If only one floor is affected by the

removal of shores for either Phase 3a or 3b, the load on that

floor slab may be determined by equilibrium. A flowchart for

Phase 3 which establishes whether loads are determined by equilibrium or by solution of stiffness equations, and whether Phase

3b is executed is shown in Figure 4.6.

Block 3. A determines whether a single floor or several

floors above the vacated story are affected by the shore removal.

A stiffness analysis is required only if more than one level is

affected. Details of the stiffness analysis for Phase 3a are

given below. Block 3.B checks whether the lowest level of shores

is the first story. If it is, Phase 3b is skipped. If the

lowest shored story is above the first story, then it must be

determined how many floors interconnected by reshores are

affected. This is accomplished by Block 3.C. Again, if only one

- 22 -
floor is affected, the slab force is determined by equilibrium

and if two or more floors are affected, a stiffness analysis is

required. Formation of the stiffness equations for Phase 3b is

covered below.

Phase 3a has only three possible forms of stiffness equations. A schematic diagram showing the corresponding cases

(Cases 1, 3, and 6) is shown in Figure 4.7. The flowchart for

Phase 3a is straight-forward and is shown in Figure 4.8. Block

3a. A sets the number of equations. The loop on number of equations is initialized in Block 3a. B. Block 3a. C computes the

floor number. Blocks 3a. D and 3a. E determine whether the equation is for Case 1, Case 3, or Case 6.

Phase 3b has four different cases associated with the

possible configurations (Cases 2, 5, 7, and 9). Distinction

between Cases 7 and 9 is based on whether the reshores are

grounded or not. Figures 4.9a and 4.9b illustrate the four

possible cases. The flowchart for Phase 3b (see Figure 4.10) is

identical to that of Phase 3a except for Block 3b. F which distinguishes between Case 7 and Case 9 on the basis of the lowest

reshored story.

4.2.4 Phase 4 - Reshoring of the Vacated Story

Formulation of the stiffness equations for Phase 4 is essentially the same as that for Phase 3. The only difference is

that, at the completion of Phase 3, the counter L s is incremented

by one (see Figure 4.1) so all expressions in Phase 4 which

contain L s differ from those in Phase 3. This affects Block 4.B

in Figure 4.11 and Block 4b. A in Figure 4.15. The remaining

figures (Figures 4.12, 4.13, and 4.14) are the same as the corresponding figures for Phase 3 and are included for completeness.

- 23 -
4.3 LOADING CONDITIONS

As noted earlier, a new loading condition is introduced when

a floor is cast and the remaining operations in a casting cycle

cause a redistribution of forces within the system of interconnected floors. Note that only the dead load is considered here.

The live load, which consists of workmen, equipment, etc., acts

only on the floor being cast and is assumed to be removed before

shores or reshores are removed. This section describes the

formation of loads consistent with the stiffness equation numbering as outlined in the previous section, that is, each term w^

(i = l,...,Q) is defined. Solution of the stiffness equations for

the loading described here produces the displacements needed for

the calculation of the slab and shoring system forces. The sign

convention assumed for the loads and displacements (see Figure

3.1) is positive downward.

For Phase 1, the load which is imposed is the weight of the

slab being cast. It is equal to the volume of concrete placed

times the unit weight of the concrete divided by the floor area.

This load is denoted here by (the subscript on W refers to the

phase). The load for each degree of freedom is defined by

Wj = Wj (4.1a)

and

W2

, • • • , Wq

0 (4.1b)

The load for Phase 2 is that on the reshores in the lowest

story prior to their removal and is denoted W2

. This load acts

downward on the lowest interconnected floor. The loading is

Wj, . .

.

0 (4.2a)

- 24 -
and

w

Q

= W2

(4.2b)

Phase 3 generally requires two stiffness analyses. The loading

condition for both is that carried by the lowest level of shores

before the shores are removed and is denoted by Wg. This load

acts down on the floor above the story in which the shores are

removed (Phase 3a) and up on the floor below this story (Phase

3b). Therefore, the loading for Phase 3a is

Wj , . . . ,

W

q_! =0 (4.3a)

and

Wq = w3

For Phase 3b, the loading is

W 1 = ~w3

(4.3b)

(4.3c)

and

w2

f . . . fWg = 0 (4.3d)

Note that Q is, in general, not the same for Phases 3a and 3b.

It is computed for each phase as indicated in the applicable

flowchart (Figure 4.8 or 4.10).

If the precompression ratio, P, is specified to be greater

than zero, the result of the reshoring operation (Phase 4) will

be a redistribution of forces within the structure. If P=0, this

operation will clearly have no effect. The load applied to both

the floors above and below the reshored story is equal to the

load on the shores in that story prior to their removal times P,

and is denoted by W 4 (W 4 = P x Wg). This load acts up on the

- 25 -
upper floors and down on the lower floors. Therefore, the

loading for Phase 4a is

w lf ...^Wq^-l = 0 (4.4a)

and

w

Q

= -W4

For Phase 4b, the loading is

w x = W4

(4.4b)

(4.4c)

and

W2

f « • • , Wq 0

Again, Q is computed separately for Phase 4a and Phase 4b.

(4.4d)

4.4 SLAB AND SHORE LOAD CALCULATION

The calculation of both slab and shore loads is straightforward. The only problem is in determining the appropriate

floor level for the particular degree of freedom (or equation

number). For all phases except 3b and 4b, the floor number is

given by

N = Nc + 1 - i (4.5)

in which i is the equation number and Nc is the floor being cast.

For phases 3b and 4b, the floor number is determined by

N=N

c

-Ns +l-i (4.6)

in which Ns is the number of shored stories.

-26 -
The slab load is the product of the slab stiffness and the

slab displacement (recall that stiffness is expressed in terms of

force per area / displacement). Displacements are determined by

solution of the stiffness equations for the appropriate loading.

The calculation is repeated for each of the Q interconnected

floors. The load on the n-th floor slab, F^ n , is

F^ n

= k^ u^ ( i=l , . . . ,Q) (4.7)

in which k n is the stiffness of the n-th floor, u^ is the slab

displacement for the i-th equation, and n is computed from either

equation 4.5 or 4.6 as appropriate. A slab load is positive if

it acts downward.

The shore or reshore load for a given story is computed in a similar fashion. Note that, if there are Q interconnected

floors, there are Q-l stories which contain shores or reshores.

The displacement of a shore is the difference between the displacements of the floors it connects. Thus, the load in the

shores in the n-th story, F

s n , is given by

F

s n

= k

g {u i - u i+1 ) (i = l,...,Q-l) (4.8)

in which k

g

is the shore stiffness. If the story in question

contains reshores, the load in the reshores, F

r n , is

F

r n

= k

r (u i " u i+i) (i=l,...,Q-l) (4.9)

Note that, as computed here, positive shore or reshore loads are

compressive.

- 27 -
Figure 4.1 - Flowchart for Determining Next Phase

-28 -
Figure 4.1 - Continued

- 29 -
urn w

a) Shores

grounded

b) Shores not

grounded

1 1

jf I

jf jf |

|i jf jf

c) Reshores

grounded

d) Reshores not

grounded

Figure 4.2 - Phase 1 Configurations
Figure 4.3 - Flowchart for Phase 1

- 31 -
a) More than one level

of reshores

b) A single level of

reshores

Figure 4.4 - Phase 2 Configurations
Figure 4.5 - Flowchart for Phase 2
Figure 4.6 - Flowchart for Phase 3

- 34-
Case 1

Case 3

Case 6

XX

XX

... X

XX

Figure 4.7 - Phase 3a Configuration

Figure 4.8 - Flowchart for Phase 3a

- 35 -
Case 2

Case 5

Case 7

tit ft ’ XX-** im t

II II

II II

— Case 9 —

II

XX

a) Reshores are

not grounded

b) Reshores are

grounded

Figure 4.9 - Phase 3b Configurations

- 36 -
Figure 4.10 - Flowchart for Phase 3b

- 37 -
A

<33

J [_ i r

•O

Figure 4.11 - Flowchart for Phase 4

- 38 -
Case

Case

Case

1

3

6

XX

XX

JL 1 1 1 ft L

Figure 4.12 - Phase 4a Configuration

Figure 4.13 - Flowchart for Phase 4a

- 39 -
a) Reshores are

not grounded

b) Reshores are

grounded

Figure 4.14 - Phase 4b Configurations

- 40 -
Figure 4.15 - Flowchart for Phase 4b

- 41 -
5 . EXAMPLE PROBLEMS

In this section several examples of the application of the

compressible shores analysis are presented. All the examples

relate to the eight story structure shown in Figure 5.1. Only a single bay is considered since the analysis does not include

continuity between bays. The slab stiffnesses are assumed not to

vary with age (E c is constant). Slab thickness is the same for

all floors, thus, k n

(n = 1 to 8) is constant. For the examples

where the shores, reshores, and ground are compressible a stiffness equal to twice the slab stiffness is used (k s =k r =k

g

=2k n

)

.

Rigid shores and base support are modeled by defining a very

large stiffness for the shores, reshores, and ground relative to

the slab stiffness (1000:1). A shoring scheme of two levels of

shores and three levels of reshores is used for examples 1 and 3.

The casting rate is seven days per floor for all three examples.

The results of an analysis are the floor slab loads and

shore or reshore loads for each of the four phases of a casting

cycle, as applicable, for each of the eight floors cast. Only

the loads on the slabs are presented here for illustration

purposes. The loads are expressed as a "load ratio" which is

defined as the ratio of the load on the slab (construction load

plus slab self weight) to the self weight of the slab. For

example, a computed slab load ratio of 1.75 means that the slab

load is equal to 1.75 times the self weight of the slab. The

actual load on a slab may be computed by multiplying the computed

load ratio by the self weight of the slab in psf.

A history of slab load ratio versus age of slab may be tabulated for each floor of the structure. Figure 5.2 shows a

typical plot of the slab load ratio versus age of slab for

stories one through five of the eight story building. The

maximum of the tabulated slab load ratios for a given age is used

for comparison purposes in the following examples. It is simply

the envelope of the results shown in Figure 5.2.

- 42 -
5.1 COMPARISON OF RIGID AND COMPRESSIBLE SHORES

In this first example, the analysis results for the cases of

rigid and compressible shores are compared. For both cases, the

precompression ratio is taken as zero. Figure 5.3 shows a plot

of the maximum slab load ratio versus the age of the slab. From

this figure it is seen that a maximum slab load of 1.89D is

computed where D is the self weight of the slab. From the complete analysis one can determine that this maximum occurs on the

second floor slab during casting of the fourth floor (Phase 1).

For the case of a rigid shoring system and base support (presently accepted procedure) a maximum slab load of 1.66D is found.

This load occurs on the fifth floor slab during the removal of

the lowest level of reshores (Phase 2) after casting the seventh

floor. This one example indicates that, for shore, reshore and

ground stiffnesses equal to twice the slab stiffness, a 14%

increase in maximum slab load is realized as compared to an

analysis assuming a rigid shoring system.

5.2 COMPARISON OF SHORING SCHEMES

In this example shoring schemes including either one, two,

or three levels of shores and three levels of reshores are compared. Flexible shores, reshores, and base support are used in

all cases and there is no precompression of reshores. It has

been observed by Grundy and Kabaila (4) that increasing the

number of levels of shores actually increases the maximum slab

load. This holds true in the analysis for compressible shores as

shown in Figure 5.4. For the case of a single level of shores,

the maximum slab load was found to be 1.52D. The maximum occurred at an age of 15 days. For two levels of shores, the maximum

was 1.89D occurring at an age of 14 days. And for three levels

of shores, a maximum of 1.98D was found at an age of 21 days.

Note that, although the maximum slab load increases with increased number of levels of shores, the age at which the maximum

- 43 -
occurs also increases. If the strength-gaining characteristics

of the concrete are known, it is possible to determine whether

the slabs have sufficient capacity to carry the maximum construction load at the age at which the maximum occurs.

5.3 COMPARISON OP PRECOMPRESSION RATIOS

The third example explores the effects of varying the precompression ratio. The structure shown in Figure 5.1, with a

compressible shoring system and base support, is analyzed for

precompression ratios of 0.0 (no precompression), 0.5, and 1.0.

Figure 5.5 compares the results of an analysis for no precompression and 50% precompression. It is seen that precompressing the

reshores to 50% of the load in the shores prior to their removal

reduces the maximum slab load at early ages and increases the

maximum load at later ages. In this particular case the maximum

slab load is reduced from 1.89D to 1.52D.

Figure 5.6 shows the effects of precompressing the reshores

to 100% of the load in the shores. Here the results of 50% and

100% precompression are plotted. Additional precompression again

reduces the maximum slab load at early ages and increases the

load at later ages. In this case, however, it is seen that

precompressing to 100% increases the maximum slab load to 1.97D.

Note that this exceeds the maximum load encountered in the case

of no precompression (1.89D). The age at which the maximum

occurs (35 days) is much greater than the age at which the maximum occurs for no precompression (14 days). Information about

the slab capacity as a function of the in-place strength of

concrete at various ages is required to assess the relative

safety of the two construction procedures.

- 44 -
ground

8 r

i 7,1-

I

"I

I

I '1

I 8 stories

1 bay

Ec constant

k s = = kg = 2k n (n — 1 ,..., 8 )

Figure 5.1 - Eight Story Building

- 45 -
SLAB

LOAD

RATIO

SLAB LOAD RATIO VS. AGE OF SLAB

(Floors 1 through 5)

Figure 5.2 - Plot of Slab Load Ratio vs. Age of Slab
MAXIMUM

SLAB

LOAD

RATIO

MAXIMUM SLAB LOAD RATIO VS. AGE OF SLAB

(rigid and flexible shores)

Figure 5.3 - Comparison of Rigid and Compressible Shores

- 47 -
MAXIMUM

SLAB

LOAD

RATIO

MAXIMUM SLAB LOAD RATIO VS. AGE OF SLAB

(For 1,2, and 3 levels of shores)

Figure 5.4 - Comparison of Shoring Schemes

48
MAXIMUM

SLAB

LOAD

RATIO

MAXIMUM SLAB LOAD RATIO VS. AGE OF SLAB

(0% and 50% precompression)

Figure 5.5 - Comparison of Precompression Ratios

(0% and 50% precompression)

- 49 -
MAXIMUM

SLAB

LOAD

RATIO

MAXIMUM SLAB LOAD RATIO VS. AGE OF SLAB

(50% and 100% precompression)

Figure 5.6 - Comparison of Precompression Ratios

(50% and 100% precompression)

- 50-
6 . SUMMARY

In this report, the importance of considering the compressibility of the shores in an approximate load analysis of multistory concrete construction was discussed. A model was described

for computing the loads on the slabs and shores which accounts

for the flexibility of the shoring system. The main focus of the

report was a detailed description for implementing the proposed

procedure. The overall flow of control was outlined and the

explicit form of the stiffness equations and loading for each

phase of construction was described. The information contained

herein should be sufficient to permit the reader to develop a computer-based analysis.

A computer program implementing the procedure described

herein was written at NBS. The program, written in FORTRAN, runs

on a personal computer. It takes as input the structure

geometry, concrete properties, and construction schedule. The

program then computes the loads on slabs and shores as each floor

is cast and the shores and reshores are advanced. Results are

reported after each of the four construction phases. Maximum

values are computed and listed along with their time of occurrence, after all floors have been cast.

To illustrate how such an analysis could be used to assist a construction engineer or contractor in determining the loads on

the slabs of a multistory building, three example problems were

presented. They demonstrate several of the program features

including the influence of shore and reshore stiffness on the

maximum slab loads, an evaluation of alternative construction

schemes, and the effects of various amounts of precompression in

the installed reshores.

- 51 -
7 . REFERENCES

1. Leyendecker, E. V. and Fattal, S. G., "Investigation of the

Skyline Plaza Collapse in Fairfax County, Virginia," NBS

Building Science Series 94, February, 1977.

2. AC I Standard 347-78, Recommended Practice for Concrete

Formwork, American Concrete Institute, Detroit, Michigan,

1978.

3. Hurd, M. K., Formwork for Concrete . American Concrete

Institute, Detroit, Michigan, 1979.

4. Grundy, P. and Kabaila, A., "Construction Loads on Slabs

with Shored Formwork in Multistory Buildings," Journa l of

&m£Eisan £PHgJ_et.e Ins&itl&s., Vol. 60, No. 12, December,

1963.

5. Lew, H. S., Carino, N. J., Fattal, S. G., and Batts* M. &.,

Xiiygatlgat.i.Qii ol Construction failing o£ flaxb.O-ax Cay

Coiidomni um In Q&slq.a Pfiflolu. ElPJLijte* nbs Building science

Series 145, August, 1982.

6. Blakey, B. E., and Beresford, F. D., "Stripping of Formwork

for Concrete in Buildings in Relation to Structural Design,"

Civil Engineering Transactions, Vol. CE7 , No. 2, October,

1965.

7. American National Standard - Flowchart Symbols and Their

Usage in Information Processing (X3. 5-1970), American

National Standards Institute, New York, 1971.

-52 -
Appendix A - Notation

D = self weight of slab

F

f n

= Force on the n-th floor slab

F

r n

= Force on the reshores in the n-th story

F

s n = Force on the shores in the n-th story

i = i-th stiffness equation

k = ground stiffness

y

k n

= stiffness of the n-th floor slab

k

r = reshore stiffness

k

g = shore stiffness

L r = lowest reshored story

L

s = lowest shored story

N = n-th floor

N

c = current top floor

Nr = number of reshored stories

Ng = number of shored stories

Nt

= total number of floors

P = precompression ratio

Q = number of stiffness equations

= weight of fresh concrete

W2 = load in lowest reshores prior to their removal

W3 - load in lowest shores prior to their removal

W4 = reshore load (precompression)

- 53 -
NBS-114A (REV. 2-80)

U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date BIBLIOGRAPHIC DATA

REPORT NO. SHEET (See instructions) NBSIR 84-2964 December 1984

4. TITLE AND SUBTITLE

IMPLEMENTATION OF COMPRESSIBLE SHORING ANALYSIS FOR MULTISTORY

CONCRETE CONSTRUCTION

5. AUTHOR(S)

John L. Gross

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State. ZIP)

10. SUPPLEMENTARY NOTES

(771 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information,

bibliography or literature survey, mention it here)

If document includes a significant

This report presents an analytical procedure for determining the loads on the

shoring system and supporting slabs in multistory cast-in-place concrete

construction. The procedure assumes that the slabs are supported by evenly

distributed compressible shores and reshores and employs the stiffness method

of analysis to solve for the loads on the shoring system and slabs as construction advances. The number of shores and reshores; shore, reshore and base

support stiffnesses; casting rate; and concrete strength gaining characteristics

are considered in the analysis. Details of the implementation of the shoring

analysis in the form of a computer program are presented. The strategy for

determining the next phase in the casting cycle is described and the details

are given for formulating the stiffness equations and loads for each phase.

Several example problems are presented to demonstrate the use of such a procedure in assisting to make critical decisions regarding planning of the

casting schedule and determining when fontwork can be safely removed.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) buildings; computer models; concrete construction; concrete (reinforced)

;

formwork; safety; structural analysis

13. AVAILABILITY

9 Unlimited

| | For Official Distribution. Do Not Release to NTIS

""71 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

(771 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

59

15. Price

$10.00

USCOMM-DC 6043-P80
I
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