CIVIL ENGINEERING FORMULAS

BEAM FORMULAS 79

whereTtorque
angle of twist
Llength over which the deformation takes place
Jpolar moment of inertia
Gshear modulus of elasticity

Strain Energy in Bending

For a member subjected to pure bending (constant moment)

(2.42)

(2.43)

whereMbending moment
angle through which one end of beam rotates with respect to the
other end
Llength over which the deformation takes place
Imoment of inertia
Emodulus 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.

U

EI 2

2 L

U

M^2 L

2 EI