Learning outcome 1 0a1 pte)- Control of ofections fort C. beam 1. A roof beam no

Question

Learning outcome 1 0a1 pte)- Control of ofections fort C. beam 1. A roof beam not supporting or attached to nonstructural partitions that are likely to be damaged by large deflections is subjected to a dead load wo 0.6 k/ft, including its own self weight and a roof live load WLR 0.5 k/ft. The beam is a cantilever, with a length of 14 ft. See section and materials below. Check if the deflection is below the maximum permissible deflection of the ACI 318 code. (9 pts) 3" psl Gr. 60 steel 3#8 18 12"

Explanation / Answer

Width of beam is 12'

Depth of beam is 18'

Moment of inertia of beam is 12 X 183/12 = 5832 in3

Fc = 5000 psi = 34.47 Mpa

Youngs modulus of concrete is 4700 X (fc)1/2 = 4700 X (34.47)1/2 = 27594 Mpa = 4002171.3 psi

Deflection of cantilever beam is given by (WxL4)/(8EI)

W is 0.6 + 0.5 = 1.1 kip/ft = 91.66 pounds/in

Length L is 14 feet = 168 in

Therefore deflection is (91.66 x 1684)/(8 X4002171.3 X 5832) = 0.391 in

Permissible limit for cantilever deflection is L/125 = 168/125 = 1.344 in

since 0.391<1.344, deflection is within limits!

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