A simply supported rectangular RC beam is to carry a uniform factored dead load of 1.2 kip/ftand a concentrated factored live load of 16 kip at mid-span. The beam self-weight is not includedin these loads. The concrete weighs 135 pcf. The span length is 25 ft. Please find the smallestsection allowed by ACI and design accordingly. Use f c’ = 5,000 psi, f y = 75,000 psi. Theexposure is interior with no weather exposure.a. Assume an arbitrary self-weight/ft of the beam.b. Find the maximum factored bending moment in the beam.c. Set up the moment equation and solve for the beam section.d. Revise the assumption if needed.Hint: The beam section (b and h) and steel reinforcement are inversely proportional. The smallestallowable beam section will be for the largest allowable steel ration (ρmax), and vice versa. Sincethe steel ratio is fixed, two remaining variables (b, d) need to be found from the moment equations.Then, bd2 term can be solved to get an acceptable b and d combination.
A simply supported rectangular RC beam is to carry a uniform factored dead load of 1.2 kip/ft
and a concentrated factored live load of 16 kip at mid-span. The beam self-weight is not included
in these loads. The concrete weighs 135 pcf. The span length is 25 ft. Please find the smallest
section allowed by ACI and design accordingly. Use f c’ = 5,000 psi, f y = 75,000 psi. The
exposure is interior with no weather exposure.
a. Assume an arbitrary self-weight/ft of the beam.
b. Find the maximum factored bending moment in the beam.
c. Set up the moment equation and solve for the beam section.
d. Revise the assumption if needed.
Hint: The beam section (b and h) and steel reinforcement are inversely proportional. The smallest
allowable beam section will be for the largest allowable steel ration (ρmax), and vice versa. Since
the steel ratio is fixed, two remaining variables (b, d) need to be found from the moment equations.
Then, bd2 term can be solved to get an acceptable b and d combination.
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