Page 138 - Civil Engineering Formulas

BEAM FORMULAS 79

where T torque
angle of twist
L length over which the deformation takes place
J polar moment of inertia
G shear modulus of elasticity

Strain Energy in Bending
For a member subjected to pure bending (constant moment)
2
M L
U (2.42)
2EI
EI 2
U (2.43)
2L
where M bending moment
angle through which one end of beam rotates with respect to the
other end
L length over which the deformation takes place
I moment of inertia
E modulus of elasticity
For beams carrying transverse loads, the total strain energy is the sum of the
energy for bending and that for shear.

FIXED-END MOMENTS IN BEAMS

Figure 2.27 gives formulas for fixed-end moments in a variety of beams. The
format of this illustration gives easy access to these useful formulas.