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PUBLICATIONS

NBSIR 80-2010

Analysis of Construction Conditions

Affecting the Structural Response of

the Cooling Tower at Willow Island,

West Virginia

H. S. Lew and S. G. Fattal

Structures and Materials Division

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

U S. Department of Commerce

Washington, D.C. 20234

July 1980

-QC—

100

,U56

80-2010

1980

c. 2

Prepared for Occupational Safety and Health Administration

Department of Labor

A/ashington, D.C. 20001

Rttiwift Burtstt of Stiftdirtft Ukrary, E-01 A(tmin. BMg,

OCT 2 4 1980

NBSIR 80-2010 ^ (j (\

I MANALYSIS OF CONSTRUCTION CONDITIONS

AFFECTING THE STRUCTURAL RESPONSE OF , THE COOLING TOWER AT WILLOW ISLAND,

'

West Virginia ^ ^

H. S. Lew and S. G. Fattal

Structures and Materials Division

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

U S. Department of Commerce

Washington, D.C. 20234

July 1980

Prepared for Occupational Safety and Health Administration

Department of Labor

Washington, D.C. 20001

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director
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ANALYSIS OF CONSTRUCTION CONDITIONS AFFECTING

THE STRUCTURAL RESPONSE OF THE COOLING TOWER AT

WILLOW ISLAND, WEST VIRGINIA

by

H. S. Lew and S. G. Fattal

ABSTRACT

The initial investigation of the Willow Island cooling tower collapse

(NBSIR 78-1578) established that the most probable cause of the collapse

was the imposition of construction loads on the tower before the concrete

had gained adequate strength. The analysis presented herein responds

to questions outside the scope of that investigation which considered

only actual conditions existing at the time of the collapse. The present investigation shows that failure would initiate in lift 28 if the

concrete strength in that lift is 1000 psi (6.9 MPa) or less, and to

maintain a safety factor of 2.0, the concrete strength in that lift

should be 4000 psi (27.6 MPa). This study also reveals that even if an additional bolt had been introduced between each exterior jumpform beam

and the tower, the stresses would not have been relieved enough to prevent failure of lift 28. Finally, it is shown, that if the ground

anchor point of the static line had been kept at the location occupied

just prior to its last move to a location near the center of the tower,

the stresses in the shell due to construction loads would have been

relieved to the extent that failure of lift 28 would probably not have

occurred.

Key Words: Collapse; concrete; concrete strength; construction; con- struction loads; cooling tower; dynamic effects; failure;

failure investigation; hoisting loads; hyperbolic shell.

iii
Table of Contents

Page

ABSTRACT ill

1. INTRODUCTION 1 1.1 Background 1 1.2 Scope and Approach 2

2. DYNAMIC ANALYSIS OF HOISTING LOADS 3

2.1 Introduction 3

2.2 Assumptions 3

2.3 Method of Analysis 5 2.4 Load Cases Investigated 7 2.5 Discussion of Results 7

3. CONCRETE STRENGTH REQUIREMENTS IN DESIGN 8

3.1 Design Philosophy 8

3.2 Evaluation of Construction Loads 9

3.3 Evaluation of Required Concrete Strength 10

4. EFFECT OF ADDITIONAL BOLTS ON TOWER RESPONSE 13

5. EFFECT OF STATIC LINE RELOCATION ON TOWER RESPONSE 15

6. SUMMARY AND CONCLUSIONS i7

7. ACKNOWLEDGMENTS 19

8. REFERENCES 19

Iv
1 . INTRODUCTION

1 . 1 Background

On April 27, 1978, one of two natural-draft hyperbolic concrete cooling

towers at Willow Island, West Virginia, collapsed during construction,

bringing down with it a four-level scaffold system attached to the collapsed portion of the shell and killing all 51 workers who were on the

scaffold. The National Bureau of Standards (NBS) investigated the collapse on behalf of the Occupational Safety and Health Administration

(OSHA) to determine the most probable cause of the collapse.

The NBS investigation, which has been documented in detail in a preceding report [1]*, indicated that the most probable cause of the collapse

was the imposition of construction loads on a portion of the shell

before the concrete in that portion had gained adequate strength to

support these loads. The study also indicated that major components of

the hoisting, scaffolding and formwork system did not fail prior to the

collapse, and ruled out the possibility of the concrete bucket having

Impacted cathead no. 4 and thereby initiating the collapse.

Figure 1.1 is a schematic illustration of the overall shape the tower

would have assumed upon completion. The concrete was being cast at the

rate of one 5-ft (1.5-m) high lift per day. On the day of the collapse,

the casting of concrete had just begun at an elevation of 166 ft (51m)

above grade level as indicated in Figure 1.1.

Figure 1.2 illustrates the construction scheme used at the Willow Island

site. A four- level scaffolding system around both the inside and outside periphery of the shell, the six equally spaced catheads, and the

hoisting loads transmitted through the catheads, were supported by the

completed top portion of the shell, mostly by lift 28, cast the day

before the collapse occurred. It was established that the collapse did

initiate in lift 28 in the region where cathead no. 4 was located. This

occurred when a bucketful of concrete being delivered to cathead no. 4 was about midway to the top and no other hoisting was being carried

out. The chain of events reconstructed from witness statements was as follows. After the initial rupture, cathead no. 4 slowly tilted toward

the inside of the tower dragging with it lift 28 and the scaffolding

attached to it. Lift 28 continued to peel off with failure radiating

circumferentially from cathead no. 4 in two opposite directions. The entire

lift 28, together with the scaffolding, formwork, the six catheads and 51

workers plummeted to the ground on the inside periphery of the tower.

Numbers in brackets refer to the references listed at the end of this

report.

1
1 .2 Scope and Approach

Subsequent to the initial investigation, a number of questions were

raised that were not within of the scope of that investigation. This

study addresses three major questions that were raised by OSHA.

One of the questions relates to the minimum concrete strength requirement to resist the expected construction loads. Specifically, what

should have been the strength of the partially cured concrete in lift

28 so that the shell would have sufficient capacity to resist the applied

construction loads with a margin of safety consistent with established

engineering practice?

In this study, the problem is analyzed from the point of view of the

construction system designer, which takes into account possible amplification of construction loads due to dynamic effects, particularly those

inherent in the hoisting system used. The evaluation of dynamic amplification of hoisting loads, however, depends in a major way upon the manner with which the hoisting system was being operated at the time

of the collapse. Because of insufficient information, such dynamic

effects could not be assessed in the first study. However, this ommisslon did not alter the conclusions of that study because the capacity

of the concrete was exceeded even without considering dynamic effects.

Estimation of dynamic forces is a necessary and Integral part in the

design of the construction scheme used, because the required margins

of safety have to be maintained, even against peak dynamic load fluctuations. It should be noted again that while dynamic effects cannot

be evaluated precisely, it is possible to examine upper- and lower-bound

conditions within which hoisting load fluctuations can be bracketed.

These bounds are established by taking into consideration various possible modes of operation of the hoisting system.

The two remaining questions deal with certain aspects of construction

practices that are different from those present at the time of the collapse and thus were not included within the scope of the first report.

One of the questions pertains to the lowest line of bolts that would

have provided an additional point of connection between each exterior

jumpform beam and the shell near the base of lift 27. These bolts were not in place at the time of the collapse, and it is of interest to examine whether their presence would have prevented the initiation of failure in lift 28. The question is addressed by evaluating the

stresses at the critical locations in the shell with the lowest bolts

in place, and comparing these stresses with the resistance of the shell

in lift 28.

The purpose of the last question is to determine whether the collapse

could have been prevented if the anchorage point at the lower end of

the static line were kept at the previous location. The anchorage point was moved to a location nearer to the center of the tower (where it was

at the time of the collapse) after lift 25 was cast. The problem is

2
solved by establishing the spatial configuration of the static line

using the specified previous support location and an analytical procedure which closely follows the steps used in the initial Investiga

tion [ 1]

2. DYNAMIC ANALYSIS OF HOISTING LOADS

2.1 Introduction

Figure 2.1, reproduced from ref. 1, shows the hoisting system used for

delivery of concrete to the top of the tower at cathead no. 4 at the

time of the collape. The lifting of concrete is controlled by the hoist

drum operator stationed at U. From the drum, the hoist line proceeds

toward and around an interior sheave at T and an exterior sheave at Q,

up and around the two sheaves suspended from the cathead beam, and, before hoisting commences, down to a concrete hopper at B near loading

platform A at the center of the tower. The static line BG suspended

from the cathead beam and anchored to the ground functions as a guide

to the hoistline during delivery of materials. Point Bj^ represents the

anchor point of the static line before the last move to B (see sec. 5).

The initial investigation of the hoisting system documented in ref. 1 was based on a static analysis of the forces in the hoisting cable and

the static line as a function of the position of the concrete bucket at

various intervals along the static line. The analysis described herein computes forces in the hoisting cable and the static line during a lifting cycle. It takes into consideration the dynamic response of the

system based on various assumptions on operating procedures of the drum

hoist. Section 2.2 cites all the assumptions made in the analysis and

discusses their effects on results. Section 2.3 describes the procedure

used in a computer program written specifically for the dynamic analysis

of hoisting forces. Section 2.4 presents the two limiting load cases considered in the analysis by assuming the hoistline at takeoff to be

initially taut and initially slack, respectively. The results of the

analysis and conclusions drawn are discussed in section 2.5.

2 .2 Assumptions

The specific assumptions made in the dynamic analysis of hoisting forces

and the effects of these assumptions on results are as follows:

1. The hoisting system is Idealized as an undamped, linear elastic

system. All materials remain in the elastic range, and cable deformations are small. Since the concrete bucket moves about 200 feet (61 m)

during a hoisting cycle, the rigid body displacements of the cable are

not small, and therefore are considered in the analysis. Principal

sources of energy dissipation in the hoisting system are friction

damping between the cable strands, and between the sheaves and their

supports. Such energy dissipation could probably be idealized using

equivalent viscous damping of one or two percent of critical, which

will have a negliglle effect on the results.

3
2. The transverse movement of the concrete bucket in space is neglected;

i.e., the bucket is assumed to move vertically from the ground to the

cathead beam. The justifications for this simplification are discussed

below.

The actual path of the bucket is curvilinear as shown in figure 2.2.

The mass of the bucket moving along this path exerts a centripetal force

which increases the tension in the static line by a negligible amount,

as pointed out in section 6.8 of reference 1. It is also noted (section

6.7, reference 1) that the speed of the bucket was estimated at 10 fps

(3.0 m/s) and that maximum hoisting loads computed by static analysis

occurred when the bucket was about 120 ft (36.6 m) below the cathead

beam. This places the bucket within the middle third region of the. span

where the path is relatively flat and approximately parallel to the

chord to the static line. For example, within a 15-ft (A.6-m) length of

the path between points 113-132 ft (34.5-39.0 m) below the cathead beam

(a distance traversed in 1.5 sec), the bucket rotates about the cathead

sheave (figure 2.2) through an angle of 0.01 radians. The corresponding centripetal force in the hoistline is about 0.3 lb (1.3 N), which

is insignificant. Therefore, the effect of the angular velocity of the

bucket on the forces in both the static and hoisting cables was neglected

and the bucket was assumed to travel in a straight line from the ground

to the cathead beam.

The additional error introduced by neglecting the slope of the static

line and assuming the bucket to move vertically up is small as indicated

by the following. Neglecting the self-weight of the hoisting cable

which is small, the static tension in the hoistline if the bucket moves vertically up is equal to the weight of the bucket. As shown in figure

2.3, tension T in the hoistline if the bucket moves parallel to the

static line is given by

T “ Wgcos B

where B, the angle of the line with respect to vertical, has a maximum

value of 32.8°. However, in the middle third region of interest, B is

approximately 25°. Thus, neglecting the transverse movement of the

bucket overestimates T by 9 percent. The dynamic hoistline tension is

independent of B as shown in figure 2.4, and is equal to the Inertia

force on the accelerating bucket. For the load cases considered in this

Investigation (sec. 2.4), the static force comprised about 72 percent of

the total force in the hoistline, indicating that the error in the total

force due to the assumption that the path is vertical was about 0.72 x 9, or 6 percent. Also note that this error is partially compensated by the

assumption that the path of the hoistline is a straight line.

3. The hoisting cable was assumed to lie on a single straight line from

the hoisting drum to the concrete bucket. This assumption has very little

effect on the force in the holstllne. Figure 2.5 shows the idealization

of the hoisting cable as a one-dimensional structure, under gravity loads

4
acting in directions consistent with those of the original structure.

As shown in figure 2.6, the one-dimensional model gives incorrect sheave

reactions, but the cable tensions are correct. Similarly, overturning

moments on the cathead assembly are correct if computed using cable

tensions

.

4. Consistent with the initial investigation [1], the hoisting line was assumed to remain parallel with the upper portion of the static line.

As shown in figure 2.7, these lines are nearly parallel.

5. The operating procedure for the hoist is such that the stresses in

the hoisting cable are never compressive at any point along its length;

i.e., no "snapping" of the cable is permitted. The prevention of hoistline snapping is dictated by practical considerations to avoid derailment

at the sheaves or spilling of concrete during delivery. This is corroborated by witness accounts, that no snapping of the hoisting cable was noted

during the operation of the hoisting system.

6. The following quantities used in this analysis are those established

during the initial investigation [1]:

a) All cable lengths and pulley locations are as shown in figure

2.1

b) the hoisting cable has an elastic modulus of 12000 ksi (82800

MN/m^) and a cross-sectional area of 0,170 in^ (110 mm'^)

c) The concrete bucket weighs 2900 lb (1314 kg)

d) The hoisting cable weighs 0.58 Ib/ft (0.86 kg/m)

e) The maximum linear velocity of the cable at the hoist drum is

10 fps (3.0 m/s)

f) The hoist drum diameter is 16 in (406 mm).

2.3 Method of Analysis

Computation of hoisting cable forces was carried out using a computer

program developed specifically for this analysis. Given the initial

length of the cable, its elastic properties, and the locations and

masses of the sheaves, an arbitrary time history of linear cable velocities can be applied to the hoist drum. In other words, the force

applied to the drum is varied automatically as necessary to maintain

the prescribed velocity history. The equations of motion are integrated step by step, using the "constant average acceleration" method.

Hoisting cable tensions due to gravity are included in the analysis.

If the cable is idealized as being Initially taut, the weight of the

bucket is included in calculating initial static tensions. If the cable

is slack, the static weight of the bucket and its dynamic effects are

not included initially. As the bucket is hoisted, the length of the

hoisting cable decreases, changing the dynamic characteristics of the

system. This change is accounted for continuously by the program.

Program output includes the following as a function of time:

5
1. The velocity and acceleration of the hoist drum

2. The equivalent force required to move the hoist drum according

to the prescribed velocity history

3. The dynamic tension, static tension, and total tension in the

hoisting cable

a) at the hoist drum;

b) at the outside and inside cathead beam sheaves; and

c) at the bucket; and

4. The displacement of the bucket above the ground, its velocity,

and its acceleration.

In addition, the program also detects and outputs the maximum dynamic

tension occurring anywhere in the hoistline during the lifting cycle,

and the location and time at which this occurs.

After reading the input data, the program calculates the stiffness and mass matrices for the cable. Conventional truss elements are used,

resulting in a tridiagonal structure stiffness matrix. Cable masses are lumped at 20 ft (6.1 m) intervals, and equivalent masses due to sheaves

are added to the cable mass at appropriate locations, giving a diagonal

mass matrix. Preliminary investigations showed that this discretization

of mass had no effect on the accuracy of the results. The idealized

structure is as shown in figure 2.8. Initially, it has 33 degrees of

freedom, one for each node. As the drum takes in cable, the length of

the first segment is continually updated and the stiffness and mass matrices reformed. When 20 ft (6.1 m) of cable is taken in, the first

node is eliminated, and the degrees of freedom of the structure are renumbered from 1 to 32 . As the bucket rises, the process continues,

until as many as 10 of the original 33 nodes are eliminated.

The prescribed velocities are applied in the following manner. At the

start of each time Increment, the response of the system is computed

assuming no load is applied to the spool end of the cable. The resulting spool velocity is V^. Then the response of the system is recomputed

assuming a unit force applied to the hoist end, giving a hoist velocity

V, . If the prescribed velocity from the assumed velocity profile is V,

the hoist force necessary to produce it is given by

This force is applied to the hoist end of the cable, and the response is

computed. Dynamic cable tensions are computed using the stiffness of

each segment. Cable tensions due to gravity loads are calculated,

taking into consideration the displacements of the bucket. Total cable

tensions are obtained by summing up the corresponding dynamic and static

values. The process continues until the bucket reaches a height of 200

ft (61 m)

.

6
2.4 Load Cases Investigated

Load Case A; Initially Taut Cable (Refer to fig. 2.9) - Lower Bound

Condition

The hoist drum and cable have zero initial velocity and they initially

carry tension due to the static weight of the concrete bucket plus the

cable self weight. Starting from these conditions, the equivalent linear

velocity of the drum is increased to 10 fps (3.0 m/s) sinusoidally over

a time interval varying from 2 to 8 seconds. Two seconds represented

the shortest time interval which did not produce snapping of the hoisting cable. Preliminary runs showed that for a given load case, integration

time steps less than or equal to 0.025 sec gave very similar results

as long as the cable was considered initially taut. A time step of 0.025

sec was therefore used for this type of load case.

Load Case B: Initially Slack Cable (Refer to fig. 2.10) - Upper Bound

Condition

The hoist drum and cable have a prescribed initial velocity but do not

carry any initial tension. Starting from the prescribed initial velocity, the mass of the concrete bucket is Immediately applied to the

hoisting system, the weight of the bucket is Included in computing

static tension, and the hoisting drum velocity is increased to 10 fps

(3.0 m/s) over a time interval from 2 to 8 seconds. Preliminary runs showed that for a given load case, integration time steps less than or equal to 0.005 sec were required to obtain satisfactory convergence of

results, and that time step value was therefore used for this type of

load case. Based upon the assumption that the cable did not snap during

hoisting, the total force in the hoisting cable at any point along its

length was never allowed to become compressive. When the cable was considered initially slack, initial velocities exceeding 4 fps (1.2 m/s) were found to cause subsequent snapping of the cable. During the quickest

lift, in which the prescribed velocity was Increased from 4 fps (1.2

m/s) to 10 fps (3.0 m/s) in a 2-sec time interval, the total hoistline

force became slightly compressive several times for very short lengths

of time (less than 0.02 sec). These momentary compressive forces were

about 100 Ibf (445 N) in magnitude.

2.5 Discussion of Results

Table 2.1 shows the maximum values for the following forces occurring

during the hoisting of the concrete bucket:

7
1. Tension in the hoisting cable.

2. Unbalanced load applied to the cathead due to different

hoisting cable forces at each cathead sheave. This is shown

as (T^-T

2

) in figure 2.12.

As can be seen from table 2.1, the most severe loading in the hoisting

cable occurs for the case in which the cable is initiallv slack, the

maximum dynamic tension being 4.1 kips (18.2 kN) . It should be noted that

this maximum occurs when the concrete bucket has displaced 150 ft (46 m)

from the ground. Prior to this, the hoisting cable experiences repeated

dynamic tensions of about 3.5 kips (15.6 kN)

If the cathead assembly does not deflect, changes in hoisting cable

tension produce no change in the static line tension, as the hoistline

will always remain parallel to the upper portion of the static line

(fig. 2.7). However, dynamic variations in tension along the length of

the hoistline do produce overturning moments on the cathead, which lead

in turn to deflections of point G, at the top of the static line. These

deflections do influence static line forces.

According to the initial study (see table 6.1, ref. 1) the static line

tension decreases by about 12 percent (from 5.4 kips, 23.9 kN to 4.8

kips, 21.2 kN) when the elastic deformation of the cathead is considered. Table 2.1 shows that the maximum difference in the hoistline

tensions at the cathead sheaves is 1.6 kips (7.1 kN). However, as in

the case of the maximum hoistline tension, this maximum occurs only

once (initially) and the repeated maximum difference in tension at the

cathead is about 1.0 kip (4.5 kN) in either direction, when the bucket

is in the middle third region where the total load effects are greatest. Considering the governing direction (same as static line tension),

the 1.0-kip (4.5-kN) force difference produces an additional moment on

the shell but decreases the static line tension by about 2.5 percent

(12% of 1.0 kip “ 2.5% of 4.8 kips). While all of these forces would

be decreased somewhat if damping were Included in the model, they are

far more sensitive to the assumed hoisting procedures.

3.

CONCRETE STRENGTH REQUIREMENTS IN DESIGN

3 . 1 Design Philosophy

The basic requirement in the design of any structure is that it should

safely support all loads during construction and in service. The imposition of construction loads on a partially completed structure should,

therefore, be subject to the same basic consideration given to the

8
design of completed structures under service loads. For the particular

case of cooling tower construction, the designer of the construction system should first evaluate the peak construction loads, including dynamic

effects, that will be imposed upon the partially completed concrete tower;

and secondly, determine the required strength of the concrete to support

the imposed loads with a margin of safety comparable to that incorporated

in the design of concrete structures in general.

3.2 Evaluation of Construction Loads

In the Initial study [1], five basic load types were considered acting

on the tower. These were; (1) the self-weight of the tower, (2) the

dead load of the suspended scaffold and formwork system, (3) live loads

on the scaffold, (4) weight of cathead assemblies and (5) hoisting loads.

In this study, only the hoisting loads need to be reevaluated to account

for dynamic effects considered in the preceeding section.

As shown in the table 2.1 and explained in section 2.4, the lower and

upper bound values of the maximum dynamic forces in the hoisting cable

(load cases A and B, respectively) are associated with two different

hoisting procedures. From a practical standpoint, it is reasonable to assume that the bucket is brought up to speed (to 10 fps or 3 m/s) in

the least amount of time without causing snapping of the hoistline.

This represents an operating procedure which minimizes delivery time

while keeping the movement of the bucket under control to avoid mishaps

such as splashing of concrete or derailment at the sheaves. In both

load cases A and B, this minimum time Interval is two seconds (figs. 2.9

and 2.10). It should be pointed out that dynamic load effects on the

hoistline system increase as the time interval used to accelerate the

bucket decreases.

The first two columns of table 2.1 list the respective values of maximum

dynamic and total (static and dynamic) tensions in the hoistline. In

every load case this maximum tension occurs at the drum while at other

locations, including the bucket end, the maximum tension is less. Because

the dynamic component of the tension at the bucket end is assumed parallel

to the segment of the static line above the bucket, it will have no effect on the static line tension, as pointed out in section 2.5.

Among the load cases considered, the maximum tension in the hoistline is

7.0 kips (31.2 kN) and occurs under load case B. The breaking strength

of the hoistline cable (27 kips or 120 kN, see sec. 5.2, ref. 1) is

several times of this value and therefore, sufficient to resist the peak

dynamic effects considered.

At any given time during hoisting operations, the parameters T

2 - T^

and T

2 + Tj^ (fig. 2.12) provide an indication of dynamic load effects on

the shell. It is recalled that in the static analysis of hoisting loads,

tension Fj^ in the hoistline was treated as constant and therefore,

contributed mostly to axial (meridional) forces F but not to normal

forces F^ which produce overturning moments on the shell (see sec. 6.7,

9
ref. 1). In dynamic analysis, the maximum value of T

2 ~ Tj^ is of

significance because it produces additional overturning moments not

accounted for in the static analysis. On the other hand, the

difference (T

2 + T| ) ~ F^, if positive, will produce additional

axial forces which, likewise, were not accounted for in the static

analysis.

The last column of table 2.1 lists the maximum values of T

2 - for the

various dynamic load cases. For load case A, this difference and its effect

on the shell is negligible. For load case B, the maximum difference is

1.6 kips or 7.1 kN (table 2.1). However, it was noted earlier that the

static line tension due to static load is at or near its peak value when

the bucket is within the middle third region of the static line. The results

of dynamic analysis for load case B show that during the time interval when

the bucket is located within this middle third region the maximum difference

T2 - T]^ is 0.8 kip (3.6 kN) while the corresponding sum T2 + Tj^ is 3.0 kips

(13.4 kN) . However, the governing loading condition occurs when T2 + T]^ is

maximum and is equal to 7.4 kips (32.9 kN) . The corresponding difference

T2 - T]^ is 0.6 kip (2.7 kN) . These were the values used in subsequent calculations of dynamic load effects on the shell.

With a minor modification, the special purpose program developed for the

static analysis of hoisting loads (sec. 6.7, ref. 1) was also used to

compute the dynamic load effects on the shell. The program was altered

to analyze hoisting loads using different values for T

2 and Ti specified

by input. This analysis yielded the results shown in table 3.1. The

last stage in the conversion of hoisting loads (load case 5) into equivalent actions applied directly to the shell, according to the procedure

described in section 6.2 of ref. 1 leads to the results shown in table

3.2.

3 . 3 Evaluation of Required Concrete Strength

It was shown previously [1] that maximum stresses occurred in the region

of the panel bounded by the two ribs where cathead no. 4 was located.

That analysis showed that combined stresses resulting from the hoop

forces and bending moments near the top of the shell and meridional

forces and bending moments near the bottom of lift 28 exceeded the

capacity of the shell. It was concluded from that analysis that failure

of lift 28 was initiated because the strength of concrete was not adequate to develop the necessary capacity to resist the applied construction loads. The Inadequate capacity of the shell at the above mentioned

critical locations was shown by means of interaction diagrams of axial

force and bending moment. The combinations of stress resultants at the

critical locations exceeded the ultimate capacity of the cross section.

Interaction diagrams are also used herein to determine the ultimate

strength of concrete necessary to develop adequate capacity of the shell

to resist safely Imposed construction loads.

10
The failure envelope for a given reinforced concrete section may be represented qualitatively by an axial force (N) -bending moment (M) interaction diagram of the type shown by the solid curve in figure 3.1 (for

further explainatlon consult sec. 7.2 and fig. 7.1 of Ref [1]). The

design envelope, shown dotted in the figure, defines the limiting conditions required to maintain a factor of safety of 2.0 against failure.

Graphically, this means that the design curve will bisect any radial

line from the origin to the failure envelope. A particular radial

line simply represents the locus of all points for which the ratio N/M

is constant and is equal to the slope of that line. The slope of line

0-1-2 shown, for instance, is given by the ratio or N

2 /M2

* Note

that in this case and (N

2

, M

2

) represent load combinations at

the design and ultimate levels, respectively (points 1 and 2 in the figure), so that the ratios N

2

/Nj^ and M2/Mj^ have the same value as the

specified factor of safety.

The design strength of the shell should be such that the capacity of any

section of the partially completed tower exceeds the construction

load effects by a reasonable margin of safety. In this analysis a factor

of safety of 2.0 is used, and is derived by the combination of an appropriate load factor and strength reduction factor <|>. For members subjected to axial compression with flexure, the ACI 318-77 Code [2] recommends <l> values which vary between 0.7 and 0.9, depending on such factors

as the type of load effects and the amount, symmetry and layout of the

reinforcement. These values are applicable to concrete structures in

service. Considering the greater variability of strength that partially

cured concrete exhibits relative to that based on 28-day strength tests,

a strength reduction factor of <j> = 0.7 for young concrete of the Willow

Island tower is judged to be appropriate. The ACI Code also recommends

load factors in the design of concrete structures under service conditions.

Although a final decision from the code authorities on an acceptable

construction load factor has not been made, there is evidence of increasing

consensus toward adopting a construction load factor somewhere in the

range of 1.3 to 1.4. The higher value of 1.4 is adopted in this investigation recognizing the possible variability of dynamic effects on hoisting

loads Indicated in table 2.1. The division of this load factor by the

strength reduction factor of 0.7 yields the safety factor of 2.0 used

in this study.

To determine the strength of concrete which is necessary to develop adequate resistance to the applied construction loads without failure, an

iterative procedure was followed using the shell analysis program

described in section 6.9 of reference 1. This procedure was necessary

because the stress distribution in the shell varies with changes in

the stiffness of the shell. In other words, as the concrete strength

increases, the elastic modulus also increases, which in turn changes the

stress distribution in the shell. Because the rate of increase in the

elastic modulus in each of the lifts of the tower varies according to

the age of curing, a number of independent analyses are necessary to

reflect redistribution of stresses in the shell with different values of

stiffness for each lift. Changes in axial forces and bending moments

11
due to changes in the compressive strength of concrete, hence the stiffness, at a number of critical locations (A, B, C and D shovm in fig. 4.2) are listed in table 3.3 for a selected number of concrete strengths.

Note that meridional axial forces and bending moments at points A and B

decrease as the strength of concrete increases, while the corresponding

hoop values at points C and D increase. A comparison of the values of

the first two rows shows the change in axial forces and bending moments

as a result of the inclusion of the dynamic force (sec. 2.4) due to

hoisting. As seen in the table, no significant changes in axial forces

and bending moments occur.

The values listed in the first two rows of table 3.3, which are based on the 220-psi (1.52 MPa) predicted concrete strength in lift 28 at the

time of failure, are plotted on the interaction diagrams corresponding

to concrete strengths of 1000 psi (6.9 MPa) and 4000 psi (27.6 MPa) in

figures 3.2 and 3.3. In these figures the ultimate bending moment of

the shell cross section is mainly controlled by the amount of reinforcement and its location. Consequently, a substantial increase in the

concrete strength would not correspondingly increase the bending capacity

of the shell cross section.

In figure 3.2 points A and A* correspond to a combination of meridional

axial force and bending moment for location A obtained without and with

the dynamic force effect included in the analysis, respectively (first

two rows of table 3.3). A" corresponds to the case in which a factor

of safety of 2.0 is applied to the axial force and bending moment for

point A'. As in the cases of A, A' and A”, the same explanation also

applies to points B, B' and B". B''', however, corresponds to the point

which represents a combined axial force and bending moment capacity with

a factor of safety of 2.0 corresponding to a compressive strength of

4000 psi (27.6 MPa) and a modulus of elasticity corresponding to that

strength. Note that the difference between points B**' and B'* is due

to the different elastic moduli used in their calculations.

It is clearly seen from the figure that the strength of the horizontal

cross section, l.e., the cross section perpendicular to the meridional

axis, is predominantly governed by bending moment. At a compressive

strength of 1000 psi (6.9 MPa), the lower portion of the panel (point B in fig. 4.2) where cathead no. 4 was located would begin to experience

crushing of concrete. For a margin of safety of 2.0 against development

of crushing with the inclusion of the dynamic force effects, the concrete

should develop 4000-psl (27.6 MPa) strength.

In figure 3.3, points C and D correspond to a combined condition of hoop

axial force and bending moment at locations C and D of the panel, C and

D' correspond to the case where the dynamic force is included in the

computation of axial force and bending moment, and C" and D" represent

the case where a factor of safety of 2.0 is applied to the axial force

and bending moment for points C and D'. It is seen in the figure that

the vertical cross section at locations C and D would not experience

crushing at a compressive strength of concrete of 1000 psi (6.9 MPa),

12
and the minimum concrete strength of 4000 psi (27.6 MPa) that would

be required to maintain a factor of safety of 2.0 against crushing

failure at point B is well beyond the strength required to maintain

a factor of safety of 2.0 aginst crushing at location D in the shell

(point D" in fig. 3.3).

Based on the foregoing analysis it is concluded that crushing failure

would occur if the concrete strength in lift 28 is 1000 psi (6.9 MPa)

or less, and that in order to resist the applied loads with a factor of

safety of 2.0 against crushing failure of the shell the concrete

strength in lift 28 should be 4000 psi (27.6 MPa). It should be recognized

that these concrete strengths are not demarcation lines which divide ' safe

or unsafe" condition. As the strength of concrete decreases from 4000 psi,

the factor of safety will likewise decrease. The factor of safety will

approach to 1.0 as the concrete strength decreases toward the 1000 psi

level, and at that level conditions would be such that failure is iramenent.

4. EFFECT OF ADDITIONAL BOLTS ON TOWER RESPONSE

In the initial investigation of the Willow Island cooling tower collapse,

it was established that the lowest line of bolts between the exterior

jumpform beams and the shell were not in place at the time of failure.

The location of these bolts is indicated in figure 4.1 which shows a typical profile of the scaffolding and cathead assembly at the top of

the tower. The purpose of the following investigation is to assess the

effect of these bolts on the response of the tower to the applied

construction loads. This was not part of the scope of the original

report because the structure was considered as it was without any

changes that might have altered its response.

An additional line of bolts will cause a redistribution of part of the

applied loads to points below the top anchor line in lift 27 (fig. 4.1)

and thereby alter the stress resultants at the critical sections in the

shell, represented by points A through D in figure 4.2. Assuming the

bolts are in place, and noting that the applied construction loads tend

to pull the tower down and toward the inside, any shear or tensile

stresses transmitted to these bolts would indicate possible relief in

the meridional stress resultants (N , M ) at critical points A and B as well as in the hoop stress resultants (N , M ) at critical points C

and D (fig. 4.2). ® ®

As noted in section 6.3 of ref. 1, the axial stiffness of the shell is

several times that of the jumpform beams. Therefore, a compressive

force applied to the cantilever portion of the exterior jumpform beam

(fig. 4.1) will be taken up mostly by the top anchor bolt in lift 28

acting in shear. Similarly, a compressive force applied between the top

and bottom bolts in lift 28 will be shared mostly by these two bolts.

In either case, the difference will be taken up mostly by the next lower

bolt and so on, so that any shear force transmitted to the lowest bolt

in lift 27 will be negligible. Thus, it is concluded that the addition

of a fourth bolt does not alter significantly the shear forces in the

meridional direction in the remaining bolts.

The inside flange of the exterior jumpform beam, which incorporates a U-shaped rib mold (fig. 4.3), fits tightly against the concrete rib and

thus inhibits torsional deformations of the beam as well as flexural

13
deformations about its minor axis. As a result, any loads producing

these effects will remain localized. It is therefore concluded that

the presence of a fourth bolt does not alter significantly the distribution of applied torques and axial forces to the portion of the shell

above lift 27.

Flexure of both the exterior and interior jumpform beams about their

respective major axes and the associated shears are the only other

effects which remain to be considered. Therefore, the pair of jumpform

beams, together with the interconnecting anchor bolt assemblies (fig.

4.1) can now be modelled as a two-dimensional (plane) frame as shown in

figure 4.4.

In the model, all joints are assumed continuous except the hinge at node

7 which connects the top and bottom sections of the exterior jumpform

beam. The assumption of continuity does not introduce appreciable

errors in the analysis because the flexural rigidity of the anchor bolts

is very low relative to the beams. Points I, J, M and N designate the

locations of the four anchor bolts through the shell, from top to bottom,

respectively. K and L are intermediate load points in lift 28. The distance between the exterior and interior jumpform beams (top and bottom

beams in the model) with respect to the centerline of the shell is

assumed to be the distance to the respective centroids of the jumpform

beams. The actual length of the anchor bolts are therefore shorter than

those in the model. To compensate for the difference, the axial rigidity

of the actual anchor bolts is used in the analysis. The loads shown are

the same as before (sum of load cases 2 through 5, sec. 6.1, ref. 1).

The condition of compatibility imposed upon the model is that beam displacements should conform with the normal displacements of the shell.

The deflected shape of the shell relative to its normal displacement

at anchor point N is shown in figure 4.4. This curve is developed on

the basis of normal displacements of the shell obtained in the initial

study. In addition, the beams are not allowed to displace into the space

occupied by the shell between nodes 8 and 37. That is, the beam nodes

8 and greater are allowed to deflect away from the "sandwiched" shell

but not into it. This requires an iterative procedure whereby initially

some of the nodes 8 to 37 are assumed to be in contact with the shell

while the others are assumed to move away from its surface so that they are free to rotate and translate. The frame is then analyzed with the

aid of the computer and a general purpose structural analysis program

by imposing the known shell displacements at all the nodes that were assumed to be in contact with it. The results of successive analyses

are then modified by Imposing or removing the appropriate nodal displacements in a manner that maintains the above-cited compatibility requirements, until the results obtained from a particular run turn out to be

consistent with the displacement assumptions made for that run.

The results of the final analysis Indicate that the additional bolt,

assumed present at N, will develop a tensile force of 1998 Ibf (8819 N).

The actions (forces and moments) on the portion of the frame to the right

14
of the anchor bolt at J are shown in figure 4.4. It is recalled that

these actions were not present in the initial investigations because the

bolt at N was not in place. The corresponding reactions at anchor bolt

locations I and J are indicated in the same figure. These reactions are

calculated by assuming I and J are simple supports, similar to the procedure used in the Initial Investigation (see sec. 6.3 of ref. 1).

Table 4.1 compiles the sum of external actions on the shell. These were

obtained by combining the actions corresponding to load cases 2 through

5 tabulated in figure 6.6 of reference 1. In table 4.1, the figures

shown in parentheses are the revised forces at I and J in the x direction

(normal to the shell) as a result of the addition of a bolt at N. They

are obtained by combining algebraicaly the reactions at I and J shown in

figure 4.4 with the tabulated forces (those without parentheses) from

the initial study. None of the other actions is altered for reasons

discussed earlier in this section.

Note that the addition of a bolt at the base of lift 27 (location N,

fig. 4.4) reduces the magnitudes of the forces at I and J in the normal

direction by about 10 and 22 percent, respectively, while leaving the

other actions unaltered. An analysis of the shell using the new set of

loads in table 4.1 as input together with the SHORE III program (see app.

B, ref. 1) yields the stress resultants at critical locations A through

D in lift 28 (see fig. 4.2). The meridional stress resultants (M^, N^)

at A and B are shown on the interaction diagram of the concrete section

at these points in figure 4.5. The corresponding results of the initial

study (without the lower bolt) are shown in the same figure for comparison. In a similar manner, the hoop stress resultants (Mq, Ng) at

C and D are plotted in figure 4.6 along with the corresponding results

from the initial study.

A comparison between the two sets of results Indicates that failure in

lift 28 at catheat no. 4 will have occurred under the same set of construction and loading conditions even if an additional bolt was used

between each exterior jumpform beam and lift 27. Although the magnitudes of the critical stress resultants at B and D are reduced to some extent by the additional bolt, they are still well beyond the ultimate

capacity of the concrete section in lift 28 at both these locations.

5. EFFECT OF STATIC LINE RELOCATION ON TOWER RESPONSE

The ground anchor point of the static line was moved to a point near

the center of the tower base on April 17, 1978. Lift 26 was the first

section of the tower placed on April 19, 1978, after the ground anchor

point had been moved. Lift 27 was placed on April 24, 1978, 5 days

after the placement of lift 26, and lift 28 was placed on April 26,

1978, 2 days after the placement of lift 27. Failure in lift 28 occurred

when lift 29 was being placed on April 27, 1978. Lift 28 was the first

section of the tower which was cured for less than one day prior to

formwork removal after the ground anchor point had been moved to the

center of the tower base.

15
The analysis of the effect of moving the ground anchor point of the static

line at its previous location on the magnitudes of the critical stresses

in the shell closely parallels the procedure in the first study and consists of four basic steps: (1) definition of geometry and stress-free

length of the static line; (2) evaluation of maximum hoisting loads using

the special purpose cable analysis program developed in the first study;

(3) evaluation of the stress resultants in the shell using the SHORE III

shell analysis program; and (4) comparison of the stress resultants with

the previously established sectional capacity of the concrete shell.

Figure 5.1 shows the geometric layout of the static line. Point

represents the position of its ground anchor point before the last move

to position B following the casting of lift 25. The space coordinates

of point Bj^ were calculated on the basis of field survey data supplied

by OSHA. To assist in the visualization of the hoisting and scaffolding

system setups, figures 6.3 and 6.1 in reference 1 have been reproduced

as figures 2.1 and 2.7 in this report with slight modifications to reflect

the shift in position from B to B^.

The criterion for deriving the stress-free length of the static line can

be visualized by reference to figure 2.7. With the concrete bucket at

the unloading position shown, and the static line assumed tensionless

but without play for that position, the stress-free length is represented by the line GKB^, as shown. This length can be calculated from

the known coordinates of points G and B^ (fig. 5.1) and the position

of point K which is also known. The stress-free length of the static

line calculated according to this procedure is 196.36 ft (59.89 m).

It should be noted that the stress-free length of the static line used

in the initial investigation was obtained by direct measurements in the

field. However, the calculated length according to the above criterion

turned out to be almost identical to the measured length, the difference

being 0.02 ft (6 mm). There are practical considerations that limit the

tolerance in the amount of play in the static line as discussed in section 6.7 of reference 1. Therefore, the calculated stress-free length

of 196.36 ft (59.89 m) is sufficiently accurate for the purpose of this

analysis.

Because the procedure from this point on is identical to that described

in reference 1, only the results will be discussed. Figure 4.2 shows

the locations in lift 28 where the calculated stress resultants are maximum. At points A and B, the meridional stress resultants (N^, M^j,)

govern.

t Figure 5.2 shows the Interaction diagram for the concrete strength f^ = 220 psl (1.52 MPa) defining the failure envelope for horizontal concrete

sections of unit width at points A and B. The maximum calculated stress

resultants (N^^, M^) at these points are plotted in the same figure as indicated. As both these points fall well within the failure envelope,

it is concluded that, with the static line anchor at B^ the construction

loads will not produce failure in lift 28 along the horizontal plane

16
through points A and B which represent locations where the most critical

meridional stress resultants occur in the shell.

Figure 5.3 shows the failure envelope for vertical concrete sections of

unit width at the level of points C and D for f^ = 220 psi (1.52 MPa).

The maximum hoop stress resultants (N^, Mg) induced at these points

are plotted in the same figure as shown. It is noted that both these

points lie within the region defined by the solid line interaction diagram

which has been developed based on the assumption that no splicing of

horizontal bars occurs within the region of interest (points C and D

in this case). If it is assumed that splicing of horizontal bars occurs

in the critical region of interest, the sectional capacity will be represented by the dotted Interaction diagram shown in the same figure. It

is seen that even if splicing occurs, the induced stress resultants at

points C and D would still fall within the capacity of the concrete

section. However, in view of the proximity of point D to the failure

envelope, a slight overstress could cause local crushing of the concrete

section in the vertical plane in that region.

The possibility of excessive radial shear stress resultants on horizontal

and vertical sections at the critical points were also investigated. The

induced shear stresses were found to be approximately within 50 percent

of the available sectional shear capacity. The procedure followed was

that described in section 7.3 of reference 1. The possibility of shear

failure was therefore ruled out.

In the light of the foregoing discussions, the following conclusions may

be drawn. If the base anchor point of the static line had been kept at

its previous location (before the last move to near the center of the

tower), the effects of the construction loads would have been reduced to

such an extent that failure of lift 28 of the tower would probably not

have occurred.

It must be recognized that in the above analysis, possible dynamic

effects on the hoisting loads were not considered because of insufficient

factual information. However, as indicated by the analysis discussed in

section 3, such dynamic effects will only slightly amplify the stress

resultants in the shell. Consequently, thes,^onclusions cited above will

not be altered by consideration of dynamic load effects.

6. SUMMARY AND CONCLUSIONS

The analysis presented in this report responds to questions on various

construction aspects of the Willow Island cooling tower that were not

part of the scope of the original investigation [1]. That investigation

considered conditions as they existed at the time of the collapse in

order to determine its most probable cause while this analysis goes beyond that investigation by considering changes to those conditions and

their effect upon the response of the tower. It should be emphasized

that all of these investigations and conclusions drawn are valid only

17
for the specific case of the tower analyzed. The questions in this

investigation address the following specific topics:

1. The strength of concrete that would be required in lift 28 of

the tower in order to resist the applied loads with a reasonable factor of safety and with due consideration given to the

dynamic nature of the loads.

2. Possible effects of an additional line of bolts between

exterior jumpform beams and the shell at the base of lift 27

3. Possible effects of a shift of the anchorage point of the static

line back to the location just prior the last move to the center

of the tower.

To answer the first question, hoisting loads were modified to include

dynamic effects which were evaluated by a separate analysis. Next, the

stress resultants in the shell due to the revised loads were determined

by analysis and were compared with the resistance of the shell for each

increment in the compressive strength of the concrete throughout the

shell profile. Because the stiffness of the shell increases with compressive strength, an iterative procedure was followed that took into

account changes in both strength and stiffness. The results of this

analysis showed that crushing failure would initiate in lift 28 if the

concrete strength in that lift is 1000 psl (6.9 MPa) or less. On the other hand

to maintain a factor of safety of 2.0 against crushing failure, the concrete

in lift 28 should have been allowed to develop a comprehensive strength

of 4000 psl (27.56 MPa).

To answer the second question, the problem was analyzed with the lowest

bolt in place by using a two-dimensional rigid frame model to represent

one of the two pairs of jumpform beams, as well as the four interconnecting anchor bolts through the shell. The model was subjected to the con- struction loads and constraints corresponding to the normal deflections

of the shell determined in the initial study [1], as well as to con- straints that did not allow the displacement of any part of the jumpform

beams into the shell. The results of this analysis indicated that due

to the presence of the additional bolts in lift 27 the magnitudes of

the critical stress resultants were reduced to some extent, but were

still well beyond the ultimate capacity of the concrete section in lift

28. It is therefore concluded that even under these conditions, the

concrete in lift 28 would have failed.

To answer the third question, an analysis was performed following the

steps of the initial investigation, with the ground anchor point of the

static line moved back to the location prior to its last move. The

results of this analysis indicated that if the base of the static line were kept at its previous location, the critical stress resultants would

have been significantly less than the ultimate strength of the concrete

section in lift 28. It is therefore concluded that the concrete in

18
lift 28 would probably not have failed and consequently, collapse would

not have occurred.

7 . ACKNOWLEDGEMENTS

The authors wish to express appreciation for the encouragement and support of this study received from Dr. R. Hays Bell of the Occupational

Safety and Health Administration, the Department of Labor.

Computer analysis of the shell presented in this report were carried by

Dr. T. A. Relnhold. The authors are grateful for his efforts.

8. REFERENCES

1. Lew, H. S., Fattal, S. G., Shaver, J. R., Relnhold, T. A., and

Hunt, B. J. , "Investigation of Construction Failure of Reinforced

Concrete Cooling Tower at Willow Island, W. Va.," NBSIR 78-1578,

National Bureau of Standards, Washington, D.C. 20234, November

1979.

2. ACI 318-77, "Building Code Requirements for Reinforced Concrete,"

American Concrete Institute, Detroit, Michigan, 1977.

19
Table 2.1 Summary of maximum forces in the hoistline (kips)

Loading Description Load Case

Hoisting Cable Cathead

Maximum

Dynamic

Tension

Maximum

Total

A Tension

Maximum

Unbalanced

Load

Initially taut cable initial

velocity = 0 fps accelerated

to 10 fps in 2 sec. A 1.1 4.0 0.02

Initially slack cable initial

velocity = 4 fps time interval

to 10 fps = 2 sec. B 4.1 7.0 ± 1.6

(1 kip = 4.A5 kN)

A Maximum total tensions occur at the hoisting drum.

20
Table 3.1 Cathead forces and reactions due to

dynamically amplified hoisting loads

(revised load case 5)

Impact Factor 3.472.9 = 1.17

Support Condition at G Elastic

Wg - weight of bucket 3400 (1540)

Sq - stress-free length of static line 219.17 (66.80)

Fjj - tension in hoistline 2942 (13092)

T - tension in static line 4766 (21209)

F - tension in counterstatic line 10511 (46774)

' cathead leg 17681 (78680)

Bp - reaction 931 (4143)

4 - components 3277 (14583)

(fig. 6.12, ref. 1) 181 (805)

H

- static line chord lengths below 90.00 (27.45)

^2 and above bucket (fig. 6.10, ref.l) 128.56 (39.21)

Units Force; Ibf (N)

Weight; lb (k,g)

Length; ft (m)

Table 3.2 Load case 5 - revised hoisting loads

\,Location

Forces I J K L

Fx (Ibf) -19819 12766 422 3075

Fy (Ibf)

F^ (Ibf)

-2199 -2199 0 0

2302 -2302 758 -1602

M (ft-lbf) 829 829 1291 2194

(1.00 Ibf = 4.45 N, 1 ft-lbf = 1.36 WM)

* Actions and location of points defined in

Figure 6.6, Ref. [IJ.

21
Table

3.3

Change

in

axial

forces

and

bending

moments

due

to

increasing

compressive

strength

of

concrete* (I a CM 00 CO nO

vn i-M 0 CM 0 CD| • • • • • • S a vO ON CM lO ON i-M •H 00 00 00 ON

Q

1“^ ON x> CM rM

<D

a ON ON Mf 30 CO nO Z -H • • • • • • CM <} m

cn CO CO CO CO CO

a

•H 30 0 r-M 00

® 1 '3- vO r-M 0 X a • • • • • • •H CM CM nO 0 lO

rH i-M

a

r—

0 0 >a- CO 0

<x>

a IT> ON CO vO Z .H • • • • • • 00 ON 0 CM CM (N CM CM CO CO CO a

q.*H CM CM CM 00 CO m 30 30 m 30 rH a • • • • • •H ON CM 0 30 uo m

00 ON C3N 30 00 00

00 CO CO CM z 00 30 00 • • • • ' • • CO CO CO CO CO CO a r-M ON 30 m CO NO

CO vO

m NO 1 • • • • • •

sJ- vO CO 0 NO ^ -H m UO m UO 0 <

CM vO CO 0 m

0-'=^ 0 0 0 0 0 0 • • • • • • 0 0 0 0 0 0 I I I

(U> •K iJ »C

mprss t

reng psi

220 220 500 1000 0

CM

4000 0 c/3 CJ

a0

•H

4-1 0

<U

CO

C>0 . C0 6

rH "e

4-1 1 4-1 z 1 rH

Cti CO• CJ 0 0

II

U

:3 4-1 CJ 4-1 0 '—

0 c

•H

cn 1 4-1 a

Hi •H

(1) .X e0 0 s • rH C • «0 0

cn

(U Z

CJ .X 0 NO

4-1 • 1—

1—

ccJ •H It X

cO 4J

M-l

4-10 a•H

CO

(U3 0 rH • CO iH > >w/

'O • • 0) iH

4-1 fH

cO 0) rH0 w

.0

CO 4-( H 0 *

22

**

With

the

exception

of

the

first

row

of

data,

tabulated

values

include

the

effects

of

the

dynamic

forces

in

the

hoisting

cable.
II

l'

Table 4.1 Sum of external loads on the shell

^\Locat ion

Forceps. I J K L

-20655

(-18501)

13234

(10250)

494 2970

'y -6320 -6320 0 0

2364 -2274 778 -1610

My* 865 864 1344 2206

* Near side jumpform beam

(force at far side equal and opposite)

Units: Moment in ft-lbf (1.00 ft-lbf = 1.36 N*M)

Force in Ibf (1.00 Ibf * 4.45 N)

Numbers in parentheses are revised forces

assuming lower line of bolts is in place

23
24
Cathead

crane

CN

(UM3

60

•H

pH

25

Schematic

view

of

construction

and

hoistion

system

layout
FIELD

DATA

u.

«o

00o

too<

UJX<ooX

<Dz

UJ e0) 4JXXMC

•H

4-1 X

•HO

4J3O

rt

i-J

CM0) J-i 3

00

•H

Pv,

[I 26
1 ft = 0.305 m

Figure 2.2 Path of the bucket

f FDYM

/inertia force on ^

ACCELERATIN6 BUCKET

Figure 2.3 Hoistline tension due

to static loads

Figure 2.4 Hoistline tension due

to dynamic loads

27
HOIST DRUM

C 1

4

BUCKET

WEIGHT

3

CABLE WEIGHT

DUE TO GRAVITY

1

HOIST —DRUM

O 2

2

GRAVITY

e 3

G 4.

GRAVITY

W BUCKET WEIGHT

(a) Original Structure (b) Idealized Structure

Figure 2.5 Idealization of hoisting cable as a one-dimensional system

(a) Original Structure (b) Idealized Structure

Hgure 2.6 Sheave reactions of actual and

idealized systems

28
SLIDE PLATE ASSEMBLY

Figure 2.7 Detail of static and hoist lines

29
SHEAVE AT

INSIDE END

OF CATHEAD

BEAM

t

SPOOL

t

SPOOL

32

33 0

200 ft

BUCKET

SHEAVE AT

INSIDE END

OF CATHEAD

^

BEAM

31

180 ft

320-*— BUCKET

Initial Configuration (b) Renumbered Configuration

after Eliminating One Node

Figure 2.8 Node renumbering during analysis

30
i 1

1.0 fps = 0.305 m/s

Figure 2.9 Assumed velocity profile,

load case A - initially taut cable

EQUIVALENT

LINEAR

VELOCITY

OF DRUM

(fps)

1.0 fps = 0.305 m/s

Figure 2.10 Assumed velocity profile,

load case B - Initially slack cable

K.

31
10

EQUIVALENT

LINEAR

VELOCITY

OF DRUM

TIME

1.0 fps = 0.305 m/s

Figure 2.11 Assumed velocity profile,

load case C - braking force

applied to taut cable

Figure 2.12 Unbalanced forces on cathead beam

32
33

Figure

3.1

Flexure

-

compression

interaction

diagram

for

concrete

beam-columns
EI M ' c c o o

•H tH

03O

O 0) O CO I—I

(U

U 4J ^

os q; 03

•W

C

C

O VO

03

O •

I—I IW CN 3 O

CO T3

cu >>

C

3^ 4-t 03

CO

COO OV

CO 03 • QJ O-vO

>-i 03 U O

CO -H

(U CO iH 4-) CL

03 OS CEO O -H O

•H

W

T3 >—I <r

•H 3

3-1 T3

(U (U

C E x:

4-1 vw

O

0X3 0 4-t O C >H rH o 5

CO II •H pq

3-1 - O

03 03 C4-4 a c E 03 n o o

CJ < 4-1

CN

(U

3-1 3

bO

•H

P4

di)| ‘<t>u

34
35

Figure

3.3

Comparison

of

hoop

stress

resultants

at

locations

C

and D

with

the

ultimate

capacity

of

concrete

section

for f=

1000

and

4000

psi

(6.9

and

27.6

MPa)
Cathead gantry

Kij?ure 4.1 Cross section through formwork and scaffolding

system

36
37

Figure

4.4

Analytical

model

of

jumpform

beam-anchorage

assembly

and

results
CATHEAD GANTRY

No 4

Figure 4.2 Location of maximum hoop and meridional stress resultants

in lift 28 (points C,D and A,B, respectively)

Figure 4.3 Sectional configuration at the interface

of exterior jumpform beam and concrete shell

38
di)|

‘ <#>N

39

Figure

4.5

Comparison

of

meridional

stress

resultants

at

locations

A

and

B

with

capacity

of

concrete

section

for

f’

=

220

psi

(1.52

MPa)

^
AO

Figure

4.6

Comparison

of

hoop

stress

resultants

at

locations

A

and

B

with

capacity

of

the

concrete

section

for

f

=

220

psi

(1.52

MPa)
BEAM

OF

CATHEAD 4

41

Figure

5.1

Layout

of

static

line

of

cathead

no.
kN-m

m

o

CO

o o

CM 00

o O

CD

ooo

o

CO

m

CO

o

c^

di)|

A2

Figure

5.2

Sectional

capacity

of

concrete

for f

=

220

psi

(1.52

MPa)

stress

resultants

at

locations

A

and

B

in

the

shell
N>l

di.)|

43

Figure

5.3

Section

capacity

of

concrete

tor

-

-^20

fsx

^

(1.52

MPa)

vs.

hoop

stress

resultants

at

l.oc

ttions

C

and

D

in

the

shell
NBS.114A (REV. a-Ts)

U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. BIBLIOGRAPHIC DATA

SHEET NBSIR 80-2010

>v ?43, ':

. - V "

v>s4. TITLE AND SUBTITLE

Analysis of Construction Conditions Affecting

the Structural Response of the Cooling Tower

at Willow Island, West Virginia

5. Publication Date July 1980

i^0odi

7. AUTHORiS)

H. S. Lew and S. G. Fattal

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

national bureau of STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON. DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fsrr»er. city, state, ZIP)

Occupational Safety and Health Administration

Department of Labor

Washington, D.C. 20001

13. Type of Report & Period Covered

15. SUPPLEMENTARY NOTES

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

1*. ABSTRACT (A 200~word or leaa factual aununary of moat significant information. If document inetudea a significant bibliography or

literature survey, mention it here.) The Initial investigation of the Willow Island cooling tower collapse (NBSIR 78-1578)

established that the most probable cause of the collapse was the imposition of

construction loads on the tower before the concrete had gained adequate strength.

The analysis presented herein responds to questions outside the scope of that

investigation which considered only actual conditions existing at the time of the

collapse. The present investigation shows that failure would initiate in lift 28

if the concrete strength in that lift is 1000 psi (6.9 MPa) or less, and to maintain

a safety factor of 2.0, the concrete strength in that lift should be AOOO psi

(27.6 MPa). This study also reveals that even if an additional bolt had been

introduced between each exterior jumpform beam and the tower, the stresses would

not have been relieved enough to prevent failure of lift 28. Finally, it is shown,

that if the ground anchor point of the static line had been kept at the location

occupied just prior to its last move to a location near the center of the tower,

the stresses in the shell due to construction loads would have been relieved to

the extent that failure of lift 28 would probably not have occurred.

17* KEY WORDS Ciilx to rweive entries; alphabetical order; capitmfiMe only the first tetter of the first key word unless a proper name;

separated by aemteolons)

Collapse; concrete; concrete strength; construction; construction loads; cooling

tower; dynamic effects; failure; failure investigation; hoisting loads; hyperbolic

shell

18. AVAILABILITY [xi Unlimited

For Official Distribution. Do Not Release to NTIS

Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

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

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

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21. NO. OF

PRINTED PAGES

47

22. Price

$ 6.00

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