Beam
Deflection by Double Integration
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* Example: The beam ABC of length L and flexural rigidity,
EI, is subjected to a uniformly distributed load as shown
below. Find the deflection of the beam
in the first half and second half of the beam. |
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Strategy: Replace the distributed load
with an equipollent, concentrated load
wL/2 acting at L/4. Use equilibrium equations
to determine support reactions. → ∑ Fx =
0, Ax =
0, ↑ ∑ Fy
= 0,
Ay + Cy ˗
wL/2
= 0 ccw ∑
MA = 0,
Cy (L) ˗ wL/2 (L/4) =
0, Cy = wL/8 (result) and Ay =
˗ Cy + wL/2 = 0
So Ay =
3wL/8 The loads acting on the
beam changes at mid-span. So break the
beam into two sections, 0
≤ x ≤
L/2 and L/2
≤ x ≤
L and construct a free body
diagram of each section to
determine the bending moment distribution for each section. Click here to continue
this example. |
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