reinforced concrete beam having the cross section shown n a simple span of 26.5 ft. It supports uniformly distributed ervice loads of 4 kip/ft live load and 1.80 kip/ft dead load excluding the beam weight). Reinforcing is as shown. etermine the maximum absolute values of the shear and ending moment. Use f'c=3000 psi and fy=60,000 psi
reinforced concrete beam having the cross section shown n a simple span of 26.5 ft. It supports uniformly distributed ervice loads of 4 kip/ft live load and 1.80 kip/ft dead load excluding the beam weight). Reinforcing is as shown. etermine the maximum absolute values of the shear and ending moment. Use f'c=3000 psi and fy=60,000 psi
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Reinforced Concrete Beam Analysis**
A reinforced concrete beam with the specified cross-section has a simple span of 26.5 feet. It is designed to carry uniformly distributed service loads: a live load of 4 kip/ft and a dead load of 1.80 kip/ft, excluding the beam's own weight. The reinforcement details are provided in the diagram. The objective is to determine the maximum absolute values of the shear force and bending moment. The concrete compressive strength is given as \( f'c = 3000 \, \text{psi} \) and the yield strength of the steel is \( fy = 60,000 \, \text{psi} \).
**Diagram Explanation**
The diagram shows:
- A vertical rectangle representing the cross-section of the beam.
- Beam dimensions: 16 inches wide and 38 inches tall.
- The top reinforcement is placed 3 inches from the compression face.
- Five reinforcement bars (each with a diameter of 1 inch) are illustrated along the tension face.
- The effective depth is indicated as 35 inches from the top compression face to the centroid of the tension reinforcement.
This layout provides critical information for calculating the shear forces and bending moments, necessary for designing safe and efficient concrete structures.
Expert Solution
Step 1: Given Data:
The span of the beam is L=26.5 ft.
The uniformly distributed live load on the beam is wL=4 kip/ft.
The dead load on the beam is wD=1.8 kip/ft.
The characteristic compressive strength of concrete is fc’=3000 psi.
The tensile strength of the steel is fy=60000 psi.
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