12.5 Method of Superposition:

)(4

4

xwdx

dEI

Recall:

The DE satisfies two requirements for superposition:

1. The load, w(x), is linearly related to deflection, (x)

2. The load does not change significantly the original geometry

How does superposition work??

1. Break beam up into series of known cases shown in App C.

2. Then tot = 1 + 2 + 3 + ……..

No solution for this case Known case from App C

Known case from App C

1.

2.

3.

How would you use superposition for these cases?

12.95 The simply supported beam carries a uniform load of 2 kip/ft. Code restrictions require the maximum deflection not to exceed 1/360 of the span length. Select the lightest-weight Z-36 steel wide-flange beam from Appendix B that will satisfy this requirement. Also, make sure stresses are acceptable if allow = 24 ksi and allow = 14 ksi.

Assume ends simply supported