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Quasi-static Response of a Timoshenko Beam Loaded by an ...

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)<br />

Q b<br />

)<br />

)<br />

s = 0.5 L<br />

)<br />

)<br />

k = 100<br />

)<br />

k = 1000<br />

)<br />

k = 1087<br />

)<br />

k = 3000<br />

)<br />

k = 5000<br />

)<br />

k = 10000<br />

)<br />

Q b<br />

)<br />

)<br />

s = 0.75 L<br />

)<br />

)<br />

k = 100<br />

)<br />

k = 598<br />

)<br />

k = 1000<br />

)<br />

k = 3000<br />

)<br />

k = 5000<br />

)<br />

k = 10000<br />

x<br />

a) b)<br />

)<br />

)<br />

s = L<br />

)<br />

x<br />

Q b<br />

)<br />

)<br />

k = 100<br />

)<br />

k = 383<br />

)<br />

k = 1000<br />

)<br />

k = 3000<br />

)<br />

k = 5000<br />

)<br />

k = 10000<br />

x<br />

c)<br />

Figure 5. Influence <strong>of</strong> the stiffness parameter k )<br />

on the shear force <strong>of</strong> the bridge Q )<br />

b , when the front <strong>of</strong> the rigid<br />

) )<br />

beam is at: a) 0.5 L , b) 0.75 L <strong>an</strong>d c) L )<br />

.<br />

25000<br />

)<br />

k<br />

20000<br />

15000<br />

10000<br />

5000<br />

Compressive<br />

forces<br />

Tensile<br />

forces<br />

0<br />

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 s ) (t) 1<br />

Figure 6. Dimension-less interface stiffness k )<br />

for which the pressure q )<br />

b becomes zero at some locations, as a<br />

function <strong>of</strong> ) s (t) .<br />

88

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