Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 249

M = WL 2 /8 (11.9)

where
M = Maximum bending moment (ft-lb).
W = Uniform weight loading per foot of the beam (lb/ft).
L = Length of the beam (ft).

■ EXAMPLE 11.10
Problem: An 11-ft-long beam supported at two points, one at each end, is uniformly loaded at a rate
of 250 lb/ft. What is the maximum bending moment in this bean?

Solution:

M = WL 2 /8 = [(250 lb/ft)(11 ft) 2 ]/8 = 3781 ft-lb

To determine the bending moment (concentrated load at center) the following equation can be used:

M = PL /4 (11.10)

where
M = Maximum bending moment (ft-lb).
P = Concentrated load applied at the center of the beam (lb).
L = Length of the beam (ft).

■ EXAMPLE 11.11
Problem: A 10-ton hoist is suspended at the mid-point of a 10-ft-long beam that is supported at each
end. What is the maximum bending moment in this beam? (Neglect the weight of the beam).

Solution:

M = PL /4 = [(20,000 lb)(10 ft)]/4 = 50,000 ft-lb

To determine the bending moment (concentrated load off-center) the following equation can be
used:

M = Pab / L (11.11)

where
M = Maximum bending moment (ft-lb).
P = Concentrated load on the beam (lb).
a = Distance from the left support of the beam (ft).
b = Distance from the right support of the beam (ft).
L = Length of the beam (ft).

■ EXAMPLE 11.12
Problem: A 10-ft-long beam supported at each end is loaded with a weight of 1400 lb at a point 2
ft left of its center. What is the maximum bending moment in this beam? (Neglect weight of the
bea m.)

Solution:

M = Pab / L = [(1400 lb)(2 ft)(8 ft)]/10 ft = 2240 ft-lb