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calculating the load required to crack a I-beam

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
moment of inertia will be calculated using parallel axis theorem I=Ic+(A*d^2) 
I=2*((12*(4^3)/12)+4*12*(13^2))+(4*(22^3)/12)=19901.33in4


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=15 in


Mcr=(474.34*19901.33)/15=629,333.1248Ib.in
=52.44 kips.ft

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

w=((Mcr*8)/(l^2))
=((52.44*8)/(28^2))
=0.53514kip/ft=535.147Ib/ft

uniform load=668.93-beam weight
=535.147-150*(2*(12/12)*(4/12)+(22/12)*(4/12))=343.48Ib/ft








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