Formwork for Concrete Structures by R.L.Peurifoy and G.D- By EasyEngineering.net

92 Chapter Five
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FIGURE 5-2 Single-span beam with uniformly distributed load.
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The maximum bending moment, which will occur at the center of
the beam, can be calculated as follows:
M = [wL/2 × L/2] – [wL/2 × L/4]
= wL 2 /4 – wL 2 /8
= wL 2 /8 ft-lb
Multiplying the preceding equation by 12 to convert the units of
bending moment from ft-lb to in.-lb, and recognizing that W = wL = wl/12,
the maximum bending moment for a uniformly distributed load on a
simply supported beam can be calculated by the following equation:
M = 12wL 2 /8
= Wl/8
= wl 2 /96 in.-lb (5-5)
If the beam is continuous over three or more equally spaced supports,
the maximum bending moment will be:
M = 12wL 2 /10
= Wl/10
= wl 2 /120 in.-lb (5-6)
Bending Stress in Beams
For a member in flexure, the applied bending stress must not exceed
the allowable bending design stress f b
< F b
. For a beam subjected to a
bending moment M, the applied bending stress can be calculated
from the following equation:
f b
= Mc/I = M/S (5-7)
For a solid rectangular beam, the moment of inertia is
I = bd 3 /12 (5-8)
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