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Example6: determination uniform load that will cause bending moment equal Mn

Determine the nominal uniform load Wn (including beam weight) that will cause a bending moment equal to Mn. fc'= 3000 psi and fy= 60,000 psi.

Figure 1







from equilibrium
T=C
As*fy=0.85*fc'*a*b
a=(As*fy)/(0.85*fc'*b)
a=(4*1.27*60,000)/(0.85*3000*16)
a= 7.47in

now we can calculate nominal moment after acquiring 'a'
Mn=As*fy*(d-a/2)
Mn=5.08*60,000*(23-7.47/2)
Mn=5871972lb-in=489.33K-ft

the maximum moment for a simply supported beam=(w*L^2)/8

(wn*L^2)/8=Mn
(wn*24^2)/8=590.93
Wn=(489.33*8)/(24^2)
Wn=6.79k/ft
Figure 2



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