Prestressed Concrete Design Using an

Electronic Digital Computer by Jan Stubbs*

Introduction

To the structural engineer the design of prestressed concr~t~ of­fers a greater challenge to his mge­nuity than a similar structure in con­ventional reinforced concrete or steel. In reinforced concrete or steel structures the forces are passive. The only possible method of de­sign is to provide sufficient ma­terial in the structure to carry the loads safely. In prestressed concrete structures the engineer is able to induce forces into the structure to counterbalance the existing forces. The choice of the method of apply­ing these counterbalancing forces is one of the fascinations of prestressed concrete. Because of this unique force system, the engineer may wish to try several possible schemes of prestressing before selecting the best one. However, complicated pre­stressed concrete structures require considerable computational effort and even the simpler structures, to be designed properly, need more calculations than a similar structure in steel or reinforced concrete.

The computation problem is made easier when it is realized that for the design of similar structural types the same procedure is always fol­lowed with the calculations being made in the same sequence. This type of problem is ideal for auto­matic solution by means of an elec­tronic computer. By breaking the structural design problems down in­to basic types, a large number of problems can be solved by the use

"Engineer, T. Y. Lin and Associates Van Nuys, California

April, 1962

of two or three different computer programs. .

Today, few structural en~meers have a detailed understandmg of the operation of electronic ?omput­ers. And in view of the rapid tech­nological advancements in the field of computers it is becoming. harder for the engineer whose basic field is not computers to keep up with computer advancements. Similarly the engineers and programers schooled in computer technology are finding it increasingly more difficult to keep up with the advancements in other fields of engineering. This communication difficulty was over­come by the writers company b~ giving a prestressed concrete engi­neer some instruction in computer operation and giving a computer pro­gramer instruction in prestressed concrete design. In this way three computer programs for prestressed concrete design were written.

Programs

(a) The first program was writ­ten for the design of simple span pretensioned prestressed concrete beams.

In this program the machine first computes the section properties of the beam, and composite sections, if any. A large number of shapes can be automatically analyzed as can be seen from Figure 1. Calcu­lations are then made at girder load, full dead load and live load for loads, shears, and moments. These are calculated at the center line, plus moments at the quarter poin~s and the minimum allowable ulti­mate moment of resistance of the

69

beam. All loads are assumed to be uniformly distributed.

The computer then assumes the number of cables as the minimum as specified by the engineer on the input form. It computes the ultimate moment of resistance of the beam according to the method outlined in the "ACI-ASCE Recommenda­tions for Prestressed Concrete and the PCI Building Code Require­ments". If this moment is less than the minimum required it increases the number of cables and repeats the calculations until the ultimate moment of resistance is greater than the required moment. It then branch­es to design either for the harped or straight cable solution.

Considering first the harped solu­tion, the machine considers the al­lowable design stresses and deter­mines the extreme positions that the center of gravity of the steel can be at the quarter points. Al­though it is realized that the quarter point is not necessarily the critical one for a strand harped only at the mid-span it is felt that errors will be small if the quarter point is used as the control section. It then solves for the losses of prestress and makes sure there are enough cables to car­ry the minimum force required with­out overstressing the cables. Next it makes sure that the eccentricity at the quarter point is within the rang­es required for elastic design.

Taking the upper limit of the ca­ble profile at the quarter point the end stresses are found. Calculations are then made to determine the de­flection under full dead load at in­finite time taking into account losses due to creep and shrinkage. If this deflection is downward the cable ec­centricity at the end is increased and the procedure repeated until the beam is flat or shows a camber

70

under these conditions. At the same time the allowable stresses are checked continually. When all of the criteria is satisfied the design of the beam is complete. Deflections for various conditions are calculated together with the principal tensile stress.

When the solution is for straight cables the machine goes through the same routine but with a check which eliminates all criteria for eccentric­ity of prestressing steel at the quar­ter points.

(b) The second program is for the design of prestressed continu­ous flat slabs. It can be used for lift slabs or slabs with haunches at the column lines and is particularly useful to the design engineer. In many cases, flat slabs contain clos­ure strips to facilitate ease of pre­stressing. A closure strip is a small gap between two separate sections of a flat slab sufficiently wide to permit a stressing operation between the sections.

These strips are closed up with a cast in place panel after the pre­stressing has been completed to form a continuous slab. The effect of these closure strips requires care­ful study and has been taken care of in the computer program. The program is designed to handle con­tinuous loads which can have dif­ferent values in the separate spans. Closure strips are considered to be point loads in the center of the span in which they occur. Just as in the hand calculation method, the machine analyzes a one foot wide strip. The distribution of forces into column and middle strips is done by the detailer. The design method gives the most economical solution for the given criteria, i.e., a slab that is perfectly flat under the full dead load, and will not be over-

Pel Journal

:

I· !I ., r B ·j .I G I. j.G .I I I ~:i

,...__ I I i .. ""'

!/ '---· . ___.J: ' ~" r...

u u

r--.---.- -,: ...,

w +4-TEE I-BEAM

,. B

.I G I •• , I ·--:::: ...._

I r~ ~ n r-:~r I

~ u

I· I· Q

~ p w U.-

* DOUBLE TEE TOPPING

I B

-1 G r- ! •j G 1-,......_·.

I 7 -~

~ ,y ~

r...

u 1 4'5 u

·-- 6

l I ..., -- ·-~ - I 7 7

~ ·I~ I· .·- •i A j .. r

-I INPUT MAY BE ANY COMBINATION OF ITEMS 1 - 7 PLUS TOPPING

INVERTED TEE

BEAM PROGRAM

SECTION - PROPERTIES COMPUTED BY MACHINE

Fig. 1 Variable cross-sections handled by the Beam Program.

April, 1962 71

stressed at any time during its work­ing life, and using the minimum amount of prestressing steel.

The machine first checks wheth­er the slab is haunched or flat. It then computes the section prop­erties of the section. If the slab is not haunched the distribution fac­tors, fixed end moment coefficients and carry over factors are computed, otherwise these values have to be read into the machine as input data.

The dead load and live load fixed end moments are computed and dis­tributed by the method of moment distribution. The position of zero shear in each span is found and the maximum midspan moments are computed. For the weight of the slab, the moments are distributed in the spans between two closure strips. The added dead load and live load are distributed over all the spans, assuming continuity through the closure strip. The closure strip is treated as a point load and the fixed end moments are distributed over the continuous spans.

The "free" bending moment due to the total dead load is computed for each span together with the avail­able drape and hence the prestress­ing force required to balance the dead load is computed. The mini­mum average prestressing stress as required by the designer is also com­puted. The machine notes whether the slab can be stressed from one or both ends and then selects the force for each span based on the computed values from above. The adjacent spans are adjusted so that the force is not reduced in the di­rection of prestressing but only equal to or greater than that required in the span farthest from the prestress­ing end. With these forces known the required drape is computed. If the required drape is greater than

72

the available drape in any one span the computor incrases the force in that span and rechecks the forces in the other spans. Whether or not a slab can be stressed from both ends is a function of the type of structure to be built. This is deter­mined by the design engineer and noted as part of the input.

The fixed end moments due to prestressed are computed and dis­tributed by the method of moment distribution. The maximum mid­span moments due to prestress are computed.

Finally the machine checks the stresses at the top and bottom, at all supports and mid-spans, and if the allowable tensile stress is ex­ceeded then the prestressing force is increased in that particular span and the minimum usable force in each span is recomputed.

An output from the slab program is shown in table 2 with an explana­tion of the notation used in table 1. This particular slab had nine interi­or spans with cantilevers on each end and a closure strip in the sev­enth interior span.

(c) The third program was written primarily for use by manufacturers of precast prestressed concrete mem­bers, where the manufacturers have forms for making standard sections. By varying the force in the member and varying the span length the same section may be used for differ­ent loading conditions. This pro­gram has been devised so that span/load tables can be automatical­ly computed. The method used is to find the greatest superimposed load a given member with a given amount of prestressing steel can carry for varying spans. This program does not go through the many intricate routines that the beam program does since the prestressing force, section

PCI Journal

profile and location of the prestress­ing steel are specified. Consequently the program is able to run through a large number of spans quickly.

The computer reads the input and first of all computes the prop­erties of the precast section. It then takes the first span and first force and determines the minimum im­posed load from any one of the following conditions:

1. Tension at full live load not greater than 80% of the average stress, i.e., 0.8 F I A where F is the final prestressing force and A is the cross sectional area of the concrete.

2. Tension at full live load not greater than 6y'f'c

.3. Ultimate moment not less than 1.2 dead load + 2.4 live load.

4. Ultimate moment not less than 1.8 (dead load + live load).

With this minimum imposed load it computes the initial d~flection of the panel and the deflection due to imposed loads. The shear stress at the supports is also computed. The computer then successively goes through all the spans with all the forces for the precast section. It then checks to determine whether a composite solution is required and

if so the properties of the composite section are computed and the whole procedure is repeated. In the case of composite design the shear stress is computed at the same cross sec­tion as in the corresponding non composite design but using the com­posite section properties.

A sample of part of the output for a load table is shown in table 4 with an explanation of the notation used in table 3. Different prestress­ing forces read across the page and different spans read down the page. From this table it is a simple matter to establish the maximum allowable imposed load for a given force and span and also to determine which force and span combinations have to be rejected on account of high shear stresses or excessive cambers or deflections.

Since few structural engineers have detailed understanding of the operations of computers, it was con­sidered essential that the input re­quired for the programs should be designed so that no knowledge of computers is needed. It was also con­sidered essential that the input be designed so that an engineer with very little experience of prestressed concrete could obtain a very sophis­ticated solution to a problem by us-

NOTATIONS AND UNITS

SPAN FORCE D DL LL MDL MTL MNET

FT FB

April, 1962

FOR SLAB PROGRAM COMPUTER OUTPUT SHEET

Span of bays in feet. Final prestressing force required per foot. Depth from top of slab to center line of cable. Total Dead Load in kips/sq. ft. Total load in kips/sq. ft. Bending moment due to total dead load, kip-ft. Bending moment due to total load, kip-ft. Bending moment due to total load minus Bending moment due to prestress, kip-ft. Stress at top fiber under full load in psi Stress at bottom fiber under full load in psi

Table 1 Slab Program Notation.

73

T. Y. LIN AND ASSOCIATES CONSULTING STRUCTURAL ENGINEERS

PRESTRESSED FLAT SLAB OUTPUT SHEET SLAB- TEST SPAN 10.00 30.00 15.00 FORCE 33.10 33.10 33.10 33.10 33.10 D 1.28 5.01 1.00 1.97 1.00 DL .09 .09 .09 TL .14 .14 .14 MDL 4.75 5.31 6.18 .68 1.55 MTL 7.25 8.06 9.43 1.03 2.37 MNET 2.50 2.88 3.27 .33 .81 FB-TL - 876.00 20.30 -1000.00 - 516.00 - 594.00 FT-TL 43.30 - 940.00 85.10 - 404.00 - 325.00

SPAN 20.00 20.00 20.00 FORCE 33.10 33.10 33.10 33.10 33.10 33.10 D 2.72 1.00 2.72 1.00 2.72 1.00 DL .09 .09 .09 TL .14 .14 .14 MDL 2.28 3.48 1.29 3.45 2.20 1.72 MTL 3.48 5.33 1.97 5.23 3.29 2.80 MNET 1.21 1.85 .69 1.78 1.09 1.09 FB-TL - 258.00 - 768.00 - 345.00 - 756.00 - 279.00 - 641.00 FT-TL - 661.00 151.00 - 575.00 163.00 - 641.00 - 279.00

SPAN 15.00 10.00 10.00 10.00 FORCE 33.10 33.10 33.50 33.50 D 1.99 1.04 1.00 1.43 DL .09 .09 .09 .09 TL .14 .14 .14 .14 MDL .57 5.42 5.59 1.05 MTL .73 7.53 7.71 1.68 MNET .16 2.11 2.12 .63 FB-TL - 487.00 - 811.00 - 818.00 - 570.00 FT-TL - 433.00 108.00 - 112.00 - 360.00 SPAN 20.00 10.00 FORCE 33.50 33.50 33.50 D 1.00 2.85 1.30 DL .09 .09 TL .14 .14 MDL 1.05 2.03 4.75 MTL 1.74 3.02 7.25 MNET .69 .99 2.50 FB-TL - 580.00 - 301.00 - 882.00 FT-TL - 350.00 - 630.00 - 48.90

Table 2 Slab Program Output.

NOTATIONS AND UNITS FOR LOAD TABLE COMPUTER OUTPUT SHEET

Wl Maximum allowable superimposed load in psf based on elastic de-sign - bottom fiber stress = + .8 favu. at total DL + LL.

W2 = Maximum allowable superimposed load in psf based on elastic de-

W3 sign - bottom fiber stress = 6 v'f;: at total DL + LL.

= Maximum allowable super imposed load in psf based on ultimate de-

W4 sign- Wuu + 1.2 DL + 2.4 LL.

= Maximum allowable superimposed load in psf based on ultimate de-sign- Wuu = 1.8 (DL + LL)

Al Intitial camber in ins. with girder load only. A2 Deflection due to the least of Wl, W2, W3 and W 4. FT Maximum shear stress with the least of Wl, W2, W3 and W4.

Table 3 Load Table Program Notation.

74 PCI Journal

> "C .... p OUTPUT FOR A LOAD TABLE ,_. (D Wl 3.66 25.19 52.87 66.70 80.54 87.46 101.30 108.22 122.06 135.90 ~ to W2 32.59 48.67 69.34 79.68 90.01 95.18 105.52 110.69 121.02 131.36

W3 19.54 35.19 54.36 63.55 72.50 76.88 85.45 89.65 97.87 105.86 W4 6.77 27.64 53.20 65.46 77.38 83.22 94.66 100.26 111.22 121.87 01 .13 .04 .06 .11 .17 .20 .26 .28 .34 .40 D2 .02 .16 .35 .42 .48 .51 .56 .59 .65 .70 FT 31.74 42.85 57.13 62.65 67.26 69.52 73.95 76.11 80.36 84.48 Wl 4.81 13.75 37.61 49.55 61.48 67.45 79.38 85.35 97.28 109.21 W2 20.13 33.99 51.82 60.73 69.64 74.10 83.01 87.47 96.38 105.30 W3 12.86 26.36 42.88 50.81 58.53 62.30 69.70 73.32 80.41 87.29 W4 2.12 15.86 37.90 48.47 58.75 63.79 73.65 78.48 87.93 97.11 Dl .22 .12 .00 .06 .13 .16 .23 .26 .32 .39 02 .04 .12 .33 .43 .52 .55 .62 .65 .72 .78 FT 29.47 39.78 53.05 59.08 64.67 66.77 70.88 72.89 76.83 80.66 Wl 11.64 4.52 25.31 35.70 46.10 51.30 61.69 66.89 77.28 87.68 W2 10.08 22.15 37.68 45.45 53.21 57.09 64.86 68.74 76.50 84.27 W3 7.48 19.23 33.63 40.54 47.25 50.54 56.99 60.14 66.31 72.31 W4 9.30 6.36 25.56 34.77 43.73 48.11 56.70 60.91 69.14 77.14 01 .35 .23 .!.:.. .08 .01 .06 .10 .17 .21 .28 .36 02 .13 .05 .29 .41 .51 .56 .66 .71 .78 .85 FT 27.50 37.13 49.51 55.14 60.48 63.09 68.20 70.25 73.93 77.50 W1 17.24 3.02 15.24 24.38 33.51 38.08 47.22 51.78 60.92 70.06 W2 1.85 12.47 26.11 32.94 39.76 43.17 50.00 53.41 60.23 67.06 W3 3.07 13.40 26.05 32.12 38.03 40.92 46.58 49.35 54.78 60.05 W4 15.18 1.41 15.46 23.55 31.42 35.28 42.83 46.52 53.76 60.79 01 .50 .37 .20 .11 .03 .00 .09 .13 .22 .30 02 .26 .04 .23 .36 .48 .53 .65 .71 .82 .91 FT 25.78 34.81 46.42 51.70 56.70 59.15 63.94 66.29 70.88 74.88 Wl 21.87 9.28 6.89 14.99 23.08 27.13 35.22 39.27 47.36 55.45 W2 4.96 4.44 16.53 22.57 28.62 31.64 37.68 40.71 46.75 52.79 W3 .58 8.56 19.77 25.15 30.38 32.94 37.96 40.41 45.22 49.89 W4 20.05 7.85 7.09 14,26 21.23 24.65 31.33 34.61 41.02 47.24 01 .70 .55 .35 .26 .16 .11 .02 .02 .12 .21 02 .42 .18 .13 .27 .41 .48 .61 .67 .79 .92 FT 24.27 32.76 43.69 48.66 53.36 55.67 60.18 62.39 66.71 70.92

Table 4 Load Table Program Output,

~

ing the computer. An example of the use of the beam program will be given to demonstrate how sim­ple it is to use these programs.

Example of a Simple Span Beam A beam is required to span 51 ft.-

0 in. as shown in Figure 2. It is proposed to use an 8 ft.-? in.

1Wi?e

single tee 28 in. deep w1th 2 Vz m. topping. The concrete topping can be used for composite action. The added dead load for partitions and the like is 120 lbs. per lineal foot of beam and the live load is 536 lbs. per lineal foot.

It is necessary to tell the machine what the allowable elastic stresses are and so these must be stated on the input form. The four critical cases are the tension at the top and compression at the bottom at trans­fer of prestress, and the tension at the bottom and compression at the top at full load. These allowable elastic stresses are defined in the code of practice and are based on the ultimate compressive stress in the concrete. In this case f~ was given as 5 ksi and hence the ulti­mate concrete stress at transfer was taken as 70% of this, i.e., 3.5 ksi. Therefore, using the "ACI-ASCE Recommendations for Prestressed Concrete and the PCI Code Re­quirements" we obtain:

a. tension at transfer = 3yf~i = 177 psi.

b. compression at transfer = 0.60f~; = 2100 psi. _

c. tension at total load = 6yf~ = 424 psi.

d. compression at total load = 0.45f~ = 2250 psi.

In this beam it was decided that hardrock concrete would be used at 150 lbs./ cu. ft. with E = 4 x 106 psi (Modulus of Elasticity). The. pre­stressing would be accomphshed

76

with Yl6 in. diameter high tensile steel wires in three rows.

The number of cable rows will normally be governed by the condi­tions at the prestressing plant and it is important to know this to get the correct cable profile.

It is well known that a pre­stressed concrete beam creeps with time. The camber in a prestressed concrete beam could increase up to 200% if left unloaded in a manu­facturer's plant for any length of time, and when loaded there will be recovery of creep. Very often de­signers neglect this effect on account of the large numbers of calculations involved. For beams to be designed properly this effect should be con­sidered. The computor program gives the engineer a choice of 1, 7, 28 or 365 days after stressing for the calculation of the deflection due to self weight, and due to added dead load. For these lengths of time a table has been incorporated in the program giving creep coefficients and stress losses.

Depending on the time at which the camber is desired to be known and also how long a beam remains in the manufacturer's plant before being placed in position and load­ed a different answer would be ob­tai~ed. In this particular beam it was decided that no additional load would be placed on the beam for 28 days so the beam load camber should be noted at that time. The instantaneous deflection due to ad­ditional dead load would be ob­served at this time also.

All that is required to design a beam has now been covered and it is a simple task to complete the input for the problem. A sample input sheet is shown in Figure 3. For simplicity for the punch opera­tor, the digits of the input are put

PCI Journal

------------------~ --- ~

Lt ve to cui • Ei7 p:s 1' ./lddeddead to~:~d • IS par

s1'- o"

ELEVATION

1--e:...o •

aol • • ~ ~

I 'I'

I I • . ,. If) ·' Ill

1--·-------------t-s"'

SECTION A-A

Fig. 2 Sample problem.

in with the first in the square to the right of the dark line with no decimal point shown. The two digits to the left of the dark line are a char­acteristic, denoting where the deci­mal point is. This is known as float­ing point arithmetic and in this case 50 denotes no digit before the deci­mal point, 51 denotes one, etc. 49 denotes 1 zero after the decimal point, 48 denotes two, etc. The pro­gram is set up for both harped strands and straight strands and each of these can be suppressed if required by placing a 1 in the ap­propriate box in line 21 of the input form.

A large number of different sec­tions can be solved automatically by the machine as indicated previ­ously in Figure 1. For double tee sections the method of calculating

April, 1962

the section properties is slightly dif­ferent than the other sections, so for these a special branch instruction is included at the bottom of the input.

All that is required of the engi­neer has now been completed and the input can then be sent to the computer center to have the input punched on cards and the prob­lem run on the machine. The solu­tion required is automatically typed out by the machine. The answer is then mailed back in the form as shown in table 6. An explanation of the symbols is shown in table 5. Sufficient information is contained on the output sheet for a draftsman to draw out the cable profile and describe all that is necessary to build the beam.

77

0 1 2 3 4 5 6 7 8 9 Addr. 1. Beam I dent. No. ~R B - ~ -~ _3_ {,_ 4 19009

.<: 'I' A T 'R 19 !:t_ 29

2. Span, ft. "i ? "i 1 39 3. Add'l DL, kips/ft. "i 0 1 !:! 49 4. Live Load, kips/ft. .5 0 5 1 6 59 5. E ksi 5 4 4 69 6. ft (GL) ksi 5 0 1 7 7 79 7. fb (GL) ksi 5 1 2 1 89 8. fb (TL) ksi _5_ 0 4 2 4. 99 9. ft (TL) ksi 5 1 2 2 "i 19109

10. f'c ksi 5 1 "i 19 11. Precast Wt kip/ftj 5 0 1 5 29 12. Topping Wt, kip/ftJ 5 0 1 "i 39 13. Cable size, inches 5 0 4 3 7 .5 49 14. Cable spacing, inches 5 0 4 3 7 5 59 15. No. cable columns _I 1 3 69 16. Min. no. cables 5 2 1 5 79 17. A no. cables 5. 1 2 89 18. Concrete Age @ GL,days _5_ 2_ _2_ 8 99 19. Concrete Age @ DL,days 5 2 2 8 19209 20. Concrete Age @ LL,days 5 3 3 6 5 19 21. 1-Point and or Straight 0 r 29 22. Section A 5 1 8 39

Dimensions B 5 2 9 6 49 Inches c "i ? ? R 59

D 5 1 1 5 69 E "i 1 1 79 F 5 1 3 89 G 5 1 8 99 H 0 19309 J -u- 19

23. Topping 0 5 1 '2 5 29 Dimensions p 5 2 9 6 39 Inches Q "[ 49

R u- 59 24. See~~QR-~------------ 4- 9.- 0- 4- 0- 0- 0- <J- -- - 19369 25. All others 4 9 0 4 0 2 4 ~

JO T. Y. LIN &,ASSOCIATES CON.ULTINQ aTRUCTUIU.L II:NGINUU

1481!18 OXNA,.D •T~tEilT

•o• VAN NUYS, CALIP'ORNIA

JO.NO \ou.•v: 'DWN.8Y _) CkD.IIY _) DAT11_ •HT o•= Fig. 3 Sample Input sheet.

78 PCI Journal

SPAN N N ULT

CABLE D-C D-E E FC MALL F F-C. FI-C SE ST FMAX FMIN FULT MACT GL DL DL + LL LDS M-C M-Q FB-C FT-C FB-Q FT-Q FB-E FT-E V-E ST DEFL DAY'S A I CB CT SB ST R2 KB KT

April, 1962

NOTATIONS AND UNITS FOR BEAM PROGRAM COMPUTER OUTPUT SHEET

Span of beam in feet Number of cables required Number of Cables required for ultimate design without con­sidering deflection criteria or maximum allowable stresses. Diameter of cable used Distance from top of beam to c.g.s. at mid span Distance from top of beam to c.g.s. at ends Modulus of elasticity of concrete at transfer Ultimate compressive stress in concrete at 28 days Ultimate resisting moment of beam or composite section Total effective force per beam in kips Effective force per cable in kips Initial force per cable in kips Maximum allowable effective stress in steel in ksi Maximum allowable transfer stress in steel in ksi Maximum allowable force per beam in kips Minimum allowable force per beam in kips Force required per beam for ultimate design Actual required ultimate moment from specifications Under condition of girder load alone Under condition of full dead load Under condition of full dead load plus live load Loads in lbs. per foot run Bending moment at center line in kip-ins. Bending moment at quarter point in kip-ins. Stress at the bottom of beam at center line in psi Stress at the top of beam at center line in psi Stress at the bottom of beam at quarter point in psi Stress at the top of beam at quarter point in psi Stress at the bottom of beam at end in psi Stress at the top of beam at end in psi Shear force at end of beam Principal tensile stress Deflection at days noted below in inches, up Days at which deflection is calculated Area in square inches Moment of inertia in inches4

Distance from center of gravity of concrete to bottom fiber Distance from center of gravity of concrete to top fiber Lower section modulus Upper section modulus Radius of gyration squared Lower kern distance Upper kern distance

General notes continued on page 80

Table 5 Sample problem input notation.

79

NOTES 1. The deflection recorded at full load plus live load is that due to in­

stantaneous live load only. 2. When composite construction is required two lines of section properties

are recorded. The properties of the beam are shown in the left hand column and those of the composite member in the right hand column.

3. + = tension, - = compression 4. Top stresses are computed at the top of precast sections in the case

of composite sections.

Table 5 (cont.) Sample problem input notation

Conclusion

The engineer in a small organiza­tion may now say that the use of a computer may be advantageous and save engineering costs but it would be impossible for his compa­ny to acquire such a machine. This was the problem facing the engi­neers and management of the au­thor's company. The problem was solved by taking advantage of a fairly recent innovation in the com­puter field, i.e., the self service com­puting center. This is a method by which several companies, large or small, can use the same computer on an hourly rate basis. In this way a very high powered computing ma­chine has been made available to the writers company with the added advantage that the company has to pay only for the actual time used.

80

It can be seen from the foregoing that an electronic computer can be used to great advantage by any or­ganization no matter how small. It does not take an extensive knowl­edge of either electronic computers or prestressed concrete to arrive at a complete and sophisticated solu­tion to a problem in prestressed concrete construction.

Acknowledgments These programs were devised in

conjunction with Computermat, Inc. of Los Angeles. The programs are written for an IBM 1620 digital computer. The theory and flow of the programs were done by engi­neers of T. Y. Lin and Associates and the programming was done by the engineers of Computermat. The work was initiated by Felix Kulka of T. Y. Lin and Associates.

PCI Journal

T. Y. LIN AND ASSOCIATES CONSULTING STRUCTURAL ENGINEERS

RB-61344 STAIR I-POINT HARPING

SPAN N N ULT CABLE D-C D-E E FC MALL

LDS M-C M-Q FB-C FT-C FB-Q FT-Q FB-E FT-E V-E ST DEFL DAYS A I CB CT SB ST . R2 KB KT

April, 1962

51.00 15.00 15.00

.43 25.12 13.68

4000.00 5.00

10913.54 GL

517.70 2019.83 1514.87

-1922.02 14.02

-1374.73 -178.00

-1452.00 -150.89

13.20 .00

-.99 28.00

497.00 33516.22

20.72 7.27

1617.00 4608.53

67.43 9.27 3.25

F F-C F1-C SE ST FMAX FMIN FULT MACT

DL 887.70

3463.39 2597.54 -658.65 -303.59 -436.00 -391.38

-1260.70 -131.01

22.63 .00

-.68 28.00

737.00 45396.90

23.50 6.99

1931.56 6487.78

61.59 8.80 2.62

Table 6 Sample problem output.

210.94 14.06 16.56

148.57 171.11 279.57 210.94 402.38

9998.27 DL+LL

1423.70 5554.59 4165.94

423.99 -510.76

375.98 -546.75

-1260.70 -131.01

36.30 39.03

.32 365.00

81