*Beam
Deflection (Statically Indeterminate)
- Method of Superposition
|
Example: Beam AB shown below is of length L and flexural
rigidity EI. It is clamped at A and supported by a rod at
B of length H, modulus of elasticity, E, and cross-sectional area A. External loading consists
of a uniformly distributed load, q. Find the axial stress in
the rod. |
|
Strategy: Determine the deflection, ∆1,
of the beam at end B in terms of q, L, and EI. Then find the defection,
∆2, of the beam at
end B in terms of T, L, and EI. The net deflection of the
beam must equal that of the rod. See
the figures below. From the value of T, the axial stress in the rod is just T/A. From tables for the beam ∆1 = qL4/8EI and
∆2 = TL4/3EI where
T is the tension in the rod For the rod ∆3 =
TH/AE Click here to continue
this example. |
| Return to Notes on Solid Mechanics |
|---|
All rights reserved.