VIII.) Deflection of Beams

A.) Reasons to Consider Deflections

B.) Assumptions in Deflection Formulas

1.) Stress does not exceed Proportional Limit

2.) Beam Material is:

a.) Homogeneousb.) Has Linear Stress-Strain Curvec.) Modulus of Elasticity is same in Tension and Compression

3.) Plane sections remain plane

B.) Assumptions in Deflection Formulas

4.) Beam has a vertical plane of Symmetry and Loads and Reactions act in this plane, perpendicular to the longitudinal axis of the beam.

B.) Assumptions in Deflection Formulas

5.) Deflections are relatively small, and the length of the elastic curve (deformed beam) is the same as the length of its horizontal projection.

B.) Assumptions in Deflection Formulas

6.) Deflection due to shear is very small therefore negligible.

C.) Using Diagrams & Formulas to Compute Deflections (Appendix H of Text)

W = Total Load (kips,N)

w = Distributed Load (kips/in,N/m)

I = Moment of Inertia (in4,m4)

l = Span Length (in,m)

x = Distance from left support to location you wish to compute deflection.

a & b are defined by the diagram.