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VIII.) Deflection of Beams
A.) Reasons to Consider Deflections
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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
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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.
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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.
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B.) Assumptions in Deflection Formulas
6.) Deflection due to shear is very small therefore negligible.
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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.