Experimental researches on composite box girders have been carried out on several bridges and test models and their structural behaviors are gradually becoming clear. The results of the measured stresses obtained at the Yamasu Bridge built in Kyoto in 1955 and the considerations of these results are described in this report. There is good agreement between the theoretical predictions and the actual behavior

FUKUMOTO, Yuhshi

KONISHI, Ichiro

YAMADA, Yoshikazu

English

Kyoto University Research Information Repository

RIGHT:URL:CITATION:AUTHOR(S):ISSUE DATE:TITLE:On the Experimental Stress Analysisof a Composite Box Girder BridgeKONISHI, Ichiro; YAMADA, Yoshikazu; FUKUMOTO,YuhshiKONISHI, Ichiro ...[et al]. On the Experimental Stress Analysis of a Composite Box GirderBridge. Memoirs of the Faculty of Engineering, Kyoto University 1958, 20(1): 1-101958-03-31http://hdl.handle.net/2433/280402On the Experimental Stress Analysis of a Composite Box Girder Bridge By lchiro KONISHI, y oshikazu YAMADA and Yuhshi FUKUMOTO De.l)artment of Civil Engineering (Received November 30, 1957) Abstract Experimental researches on composite box girders have been carried out on several bridges and test models and their structural behaviors are gradually becoming clear. The results of the measured stresses obtained at the Yamasu Bridge built in Kyoto in 1955 and the considerations of these results are described in this report. There is good agreement between the theoretical predictions and the actual behavior. 1. Purpose of Experiment For the exact understanding of the structural characteristics of the composite box girder bidges there remains many obscure points, especially in the quantitative under-standing of the stress distributions due to torsion of the box girder caused by the eccentric loading. Therefore, the main purposes of the present experiments are : ( 1 ) The measurements of the distributions of normal stress and shearing stress due to the symmetric loading. ( 2) The measurements of the distributions of normal stress and shearing stress due to the eccentric loading. 2. Details of Experiment The Yamasu Bridge is a welded single box girder bridge, and is de-signed and executed without tern- ~ I 4700 porary supports during placing of the permanent dead load. The height of web plate varies paraboli-cally having the maximum value at the span center and the cross sec-tion of the end of this bridge is shown in Fig. 1. Fig. 1. Cross Section at Span End I 2 lchiro KONISHI, Y oshikazu YAMADA and Yuhshi FUKUMOTO The main dimensions are as follows : Span length Width of bridge Steel weight 36.300m 4.500m 195 kg/m2 • The main instruments used in these measurements are three strain indicators, five switch boxes for indicator, ASKANIA hand vibrograph and two deflection meters System Tanabe. For test load two trucks, loaded with gravel, are used and each truck weight is 13.0 tons. To :measure the strains at the mid-span cross section these trucks are located near the center of the bridge (experiments No. 1-4), and to measure the strains at the end section these trucks are located near the end of the bridge ( experiments No. 5-8). The location of two trucks is shown in Table 1. The location of strain gages and its marks are shown in Fig. 2. Table 1. Experiment No. I Location of Load No. 1 Symmetric Loading Two trucks are located side by side and their rear wheels are on the center of the span. One truck is located behind another one on the down-No. 2 Eccentric Loading stream side and the rear wheel of the former truck is on the center of the span. No. 3 Symmetric Loading The loads in No. 2 are removed so as to locate them on the center part of width. No. 4 Eccentric Loading The loads in No. 2 are removed so as to locate them symmetrically about the bridge axis. No. 5 Symmetric Loading Two trucks are located side by side and their front wheels are on the section A-A one meter apart from the support. One truck is located behind another one on the down-No. 6 Eccentric Loading stream side and the front wheel of the former truck is on the section A-A. No. 7 Symmetric Loading The loads in No. 6 are removed so as to locate them on the center part of width. No. 8 Eccentric Loading The loads in No. 6 are removed so as to locate them symmetrically about the bridge axis. Z400 :1·:~'---~2 ____ 3~: : 10.....,__ ....... ...__..,..... __ ~ d -11 ~ Streflll Mid-Span Cross Section Cross Section A-A Fig. 2. Strain Gage Locations On the Experimental Stress Analysis of a Composite Box Girder Bridge 3. Measured Results 1) Normal stress a at main girder 3 Normal stress a at the mid-span cross section obtained by the experiments No. 1-4 is shown in Table 2. 2) Shearing stress -r at main girder Shearing stress -r at the end of the bridge obtained by the experiments No. 5-8 is shown in Table 3. The directions of two wire strain gages to measure the shearing stress are placed at the angle of n/ 4 with respect to the bridge axis considering that the principal stresses take these directions at the end of bridge. Table 2. Normal stress er, kg/cm2, at Span Center Table 3. Shearing Stress r, kg/cm2, at Span End Gage Experiment No. Gage Experiment No. No. No. 1 I No. 2 I No. 3 I No. 4 No. No. 5 No. 6 I No. 7 I No. 8 1 - 42.0 - 42.0 - 42.0 - 52.5 34 35 88.8 45.2 85.7 129.2 2 - 21.0 - 42.0 - 42.0 - 31.5 36 37 88.8 45.2 76.7 92.9 3 - 52.5 - 52.5 - 42.0 - 42.0 38 39 68.7 37.5 68.7 113.1 4 - 52.5 - 52.5 - 42.0 - 31.5 40 41 - - - -5 +105.0 + 84.0 + 84.0 +105.0 42 43 0 20.2 0 20.2 6 +252.0 +210.0 +210.0 +199.5 44 45 60.2 76.7 40.4 16.2 7 +262.5 +210.0 +210.0 +220.5 46 47 72.7 105.0 64.6 28.3 8 +252.0 +210.0 +210.0 +210.0 48 49 96.9 125.2 84.8 40.4 9 +263.0 +210.0 +231.0 +220.5 50 51 88.8 109.0 80.8 36.4 10 +252.0 +210.0 +210.0 +199.5 52 53 20.2 24.2 20.2 12.1 11 +105.0 + 84.0 + 84.0 + 73.5 54 55 - - - -12 - 31.5 - 21.0 - 42.0 - 52.5 56 57 16.2 20.2 20.2 28.3 The maximum shearing stress is calculated from the following equation: -r = <11 -<12 = E ( ) max 2 2(l+v) e1-e2 , where e1 and e2 are the principal strains. 4. Theoretical Stress Analysis of Main Girder The theoretical stresses are calculated ac-cording to the method given by one of the authors1 ). ..._ I !:. ~ ~ //00 ~500 'h (2) 6-a ~I; (1) /100 ~~ ,8 Fig. 3 shows the standard cross section for the calculation and it is assumed that the cross section is uniform all over the span. In this calculation the ratio of the elastic modulus of Fig. 3. Standard Cross Section I 4 lchiro KONISHI, Yoshikazu YAMADA and Yuhshi FUKUMOTO steel to that of concerete is assmed as n = 6. With this value, the satisfactory coin-cidence can be obtained for the calculated and experimental results. 1) Simple torsion Torsion function qi can be defined as (2) where q, is the shear flow on part i due to simple torsion and G. is the elastic shear-ing modulus of steel. So the torsion function qi can be calculated as follows. (3) where c11 , c12 , c22 , F1 and F2 are constants which depend on the shape and dimension of the cross section. In this bridge, we have similarly, 'q;_ = 117.46 cm2 , 'q; = 83.23 cm2 • Torsional rigidity K is expressed as and, hence 2) Shear center K = 4 C22Fr+2c12F1F~+c11Fi Gs+ :E 13 Gbt3' C11C22-C12 K = 7.22808 X 1012 kg-cm2 • (4) The vertical distance h between the shear center and the fixed point of the cross section can be obtained as follows: (5) where qh is the shear flow due to the horizontal shearing force acting to the shear center S and re is the distance between qh and point C (center of the deck). We obtain h=21.57 cm from Eq. (5), that is to say, the shear center is 21.57 cm below the center of the deck. 3) Shear flow due to bending The cross section being symmetric, the shear flow qb due to bending is given by Eq. (6), qb = - -ds, Q ~s yt I o n (6) where Q is the shearing force, I is the sectional moment of inertia of the composite girder and rs JI!_ ds is the moment with respect to the neutral axis V-V of the portion Jo n On the Experimental Stress Analysis of a C'lmposite Box Girder Bridge 5 of the cross-sectional area. The shearing stress Tb is calculated from the relation, Tb= 1 . 4) Bending torsion The warping function is defined as Ws=Ws/!!, where Ws is the warping occurred in the cross section. The warping function Ws is also shown as follows : W =- rds+ q;ngds ~s ~s -s O s O t ' where rs is the distance between the shear center and the center line of the thin-walled sections and q, is the torsion function. The warping function Ws of this bridge is obtained from Eq. (7), and its distribution is shown in Fig. 4. Bending torsional rigidity EsCw can be ob-tained by using the warping function Ws . (7) Fig. 4. Warping Function W., Cw= f Wit ds JF n = 15.1843 x 109 cm6 • 5) Stresses ab and Tb due to bending ab= "'1 Y, •b = <J!. (8) (9) The measured stresses in the experiments No. 1, 3, 5 and 7 are shown in Figs. 5(a), 5(c), 7(a) and 7(c) respectively. Experimint No. 1 252 (268) (a) 2S2 U68) 4", <i,,f,,l -- Expu,i1U11.t11,/ ---c) C•lcul~ted Experiment No. 2 1..--------(b) 6 lchiro KONISHI, Yoshikazu YAMADA and Yuhshi FUKUMOTO Experiment No. 3 Experiment No. 4 <------ -..... ----=====2~00~·!.--------l==i'OO~~==~- -<218) (2:52) _________ j ------ I ---..1 (c) Fig. 5. Normal Stress a' at Span Center 6) Stresses 1:s, 7:w and Ow due to torsion. (d) These stresses are calculated from the following equations respectively. (10) (11) _ Ws d 2fl Ow - Es - - . (12) n dx2 (,I dfJ d2fl d3fJ . dx, dx2 , and dx3 m the Eqs. (10) ~ (12) are obtained from the following equation in the case of a single load (see Fig. 6). .:x Fig. 6. {}(x) = -r;sin~a(l-c) sinhax+ r;(l-c) x+ i[sinha(x-c)-a(x-c)]-U(x-c), (13) a 3 smh al a 2l a 3 where a = ✓ K = 1.506 x 10-2 cm-1 EsCw r; = P(B-a)/EsCw. The stresses due to torsion are calculated from Eqs. (10) ~ (12) in each experi-ment as follows : a) Experiment No. 2 ~~ = 24.5232 X 10-10 , Owmax(lower cover plate edge)= Es Ws dd2~ = 16.8 kg/cm2 • n X Therefore, normal stress o is shown as On the Experimental Stress Analysis of a Composite Box Girder Bridge 7 These calculated results are shown in Table 4. Table 4. Calculated Stress ,;, kg/cm2, in Experiment No. 2 Each part at CT= CTb+CTw cross section w, CTw CTb Downsteam I (see Fig. 4) Upstrean 2 6,537 ±16.8 234.7 +251.5 +217.9 3 0 0 234.7 +234.7 +234.7 5 3,307 ± 8.5 -51.2 - 42.7 - 59.7 6 0 0 -51.2 - 51.2 - 51.2 web center 4,922 ±12.7 91.8 +104.5 + 79.l b) Experiment No. 4 The loading in experiments No. 4 and No. 2 is symmetric about the bridge axis, so we can conclude that the strees distribution in experiment No. 4 is axially sym-metric as that of the experiment No. 2. c) Experiment No. 6 Value of ~: at the point apart 1 m from the support is equal to 2.7360x 10-1• similarly, qt = Qi.Gs d{} dx = 117.46x 7.88x l05 X 2.7360x 10-1 = 25.32 kg/cm, ql 25.32 31 65 k I 2 Ts1 = t = O.S = . g cm , q2 17.94 2243k / z Tsz = T = OS = . g cm . d) Experiment No. 8 ~: = 2.9594x10-1 • Same as the experiment No. 6, qs1 = 27.39 kg/cm, qsz = 19.41 kg/cm, Therefore, shearing stress T is shown as Ts 1 = 34.23 kg/cm2 , T sz = 24.26 kg/ cm2 • These calculated stresses Tb, Ts and T are shown in Table 5, and in this case Tw is negligibly small. 8 Ichiro KONISHI, Yoshikazu YAMADA and Yuhshi FUKUMOTO Table 5. Calculated Shearing Stress 7, kg/cm2 Experiment 'T='Tb+'Ts No. 'Tb 73 I Downstream Upstream qi 59.71 ±31.65 28.1 91.4 ~ ~ q3 60.89 ±31.65 29.2 92.5 .. No. 6 qy 89.08 ±31.65 57.4 120.7 ,.,. T. -~·rv q4 88.09 ±31.65 56.4 119.7 I_ i q6 6.02 ± 9.22 -3.2 15.2 ±34.23 ~ f qi 59.71 93.9 25.5 v1 q3 60.89 ±34.23 95.1 26.7 No. 8 l qv 89.08 ±34.23 123.3 54.9 q4 88.09 ±34.23 122.3 53.9 q6 6.02 ±10.00 16.0 4.0 The comparision between the calculated stresses, a and -r, with the measured values are shown in Figs. 5(a)~5(d) and 7(a)~7(d). Experiment No. 5 Experiment No. 6 2 -stren, ~·~ :Ii@ t,6) -------- (/20) r 45 CIO'IJ \ 45 125 193> '?", '3/c.t -- E:tpeH.,enf•I ---C J Ca.lculated (a) (b) Experiment No. 7 Experiment No. 8 jll! (Iii) (c) (d) Fig. 7. Shearing Stress " at Span End 5. Consideration on Experimental Results 1) Normal stress a at main girder a) The ratios of the measured stresses to the calculated stresses at the center cross section are in case of n = 6, On the Experimental Stress Analysis of a Composite Box Girder Bridge 88% at the upper cover plate and 93% at the lower cover plate. 9 In case of n=lO, those ratios are about 70%. So n=6 can be satisfactorily applied to such a composite girder. b) From the results of calculation, we can obtain that in the experiments No. 2 and No. 4, the proportion of stress dw due to the bending torsion to stress db is 7.5% at the lower cover plate and 16.6% at the upper cover plate. From the measured stress distribution we can see that there is little influence of dw at the lower cover plate, but there is some influence of dw at the upper cover plate, i.e., about 20% to db• There is also the effect of bending torsion at the web plate and its tendency coincides well with that of calculated. c) There is very little influence of the bending torsion at the lower cover plate where the largest stress occurs. 2) Shearing stress -r at main girder a) In the experiments No. 5 and No. 7, the measured stresses coincide well with the calculated stresses as shown in Figs. 7 (a) and 7 ( c). From the results of calculation, we can obtain the following results. b) Shearing stresses -rs due to torsion are 32 kg/cm2 in the ex\>eriment No. 6 and 34 kg/cm2 in the experiment No. 8 and -rs at the neutral axis is 36% of the shearing stress 'rb, and at the web plate is 36~52% of the shearing stress •b. Therefore, the influence of the shearing stress -rs is comparatively large. c) The shearing stress -rw due to bending torsion is negligibly small in this bridge. 6. Conclusion The results and considerations of the present experiments are described in the previous sections. The main conclusions obtained in this bridge are as follows: 1) We can use the whole cross section with sufficient accuracy for the calcula-tion of stresses. 2) Composition of the concrete slab to the steel girder for live load is effective and the value n=6 is adequate for the load applied in the present experiments. 3) Influence of the bending torsion is negligibly small. 4) Influence of the simple torsion is the most remarkable. Therefore, the above method in which the influence of torsion is considered has to be used to calculate the shearing stress. 5) The result of the measurement of stresses proved good validity of the theore-tical formulae used in this report. 10 lchiro KONISHI, Yoshikazu YAMADA and Yuhshi FlIB:UMOTO 6) The experimental results of the deflection are abbriviated in this report, how-ever the experimental values of the deflection are coincided well with the theoretical values, and the ratios of those two values are about 98~100%. 7) Concerning the dynamic deflections the maximum impact factors of the bridge are about 80% when one truck run over the bridge and about 30% when two trucks run at the same time. The latter value is nearly equal to the value used in the design sheet of this bridge. 8) The vibrational characteristics of this bridge are also abbriviated in this report, however the following values are obtained. Fundamental period of vibration T = 0.368 sec (experimental value) T = 0.363 sec (theoretical value). Logarithmic decrement of vibration o = 0.066. Reference 1) I. Konishi, S. Komatsu and M. Ohashi; Stress Analysis and Calculation for Design of Com• posite Box Girder, Trans. of Japan Soc. of Civ. Eng., No. 25, 1955. 

On the Experimental Stress Analysis of a Composite Box Girder Bridge

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On the Experimental Stress Analysis of a Composite Box Girder Bridge

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