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calculating the load required to crack a rectangular beam

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calculate the uniform load(in addition to beam weight) that will cause the section in figure 1 to begin to crack if the are used for 28ft simple span.


fc'=4000psi, fr=7.5√fc' and reinforced concrete weight =150 lb/ft3.






figure 1  

for the above example, we need to calculate the value of the cracking moment. using cracking moment we can calculate the required load.

Mcr=fr*I/y    

fr=7.5√4000=474.34 psi
I=(bh^3)/12=(14*(24^3))/12=16,128in4

y is the distance from the neutral axis to extreme fiber in the tension zone. neutral axis will be located at the center of the beam due to symmetry. therefore, y=12 in


Mcr=(474.34*16,128)/12=637,512.96Ib.in
=53.126 kips.ft

the maximum moment for simply beam =(w.l^2)/8

w=((Mcr*8)/(l^2))
=((53.126*8)/(28^2))
=0.542kip/ft=542.10Ib/ft

uniform load=542.10-beam weight
=542.10-150*(24/12)*(14/12)=192.1Ib/ft


   





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