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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.


fr=7.5√4000=474.34 psi
moment of inertia will be calculated using parallel axis theorem I=Ic+(A*d^2) 

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

=52.44 kips.ft

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


uniform load=668.93-beam weight


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