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▷ Example: Determine the allowable service load: in the following. Include beam weight. PD = 2K 6 WL pommt 20ft 30000 =145 pcf 15" 4-#5 |fc²=4 ksi | 10" Fy=SOKSi ㅏ

▷ Example: Determine the allowable service load: in the following. Include beam weight. PD = 2K 6 WL pommt 20ft 30000 =145 pcf 15" 4-#5 |fc²=4 ksi | 10" Fy=SOKSi ㅏ

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Please solve this problem step by step explaining each step so it is easy to comprehend. Subject is Reinforced Concrete Design
### Example: Determining the Allowable Service Load #### Problem Statement: Determine the allowable service load in the following scenario. Include beam weight. #### Diagram A: A horizontal beam is shown with a length of 20 feet, supported at both ends. The beam has a uniform load (w) applied across its length. There is also a concentrated load (Po = 2k) at the center of the beam. #### Diagram B: A triangular truss structure is illustrated with a height of 10 feet and a base of 30 feet. The truss is supported at both ends. #### Beam Specifications: - Beam moment of inertia, I - Beam section modulus, S - Concrete strength, \( f'c = 4 \) ksi - Steel yield strength, \( f_y = 50 \) ksi #### Cross-Section of Beam: - Width = 20 inches - Depth = 15 inches - Reinforcement: 4 bars of #5 rebar at the bottom (tension reinforcement) and 5 bars of #5 rebar at the top (compression reinforcement) #### Material Properties: - Concrete: \( f'c = 4 \) ksi - Steel: \( f_y = 50 \) ksi #### Calculation Steps: 1. **Determine the Self-Weight of the Beam:** - Calculate the volume of the beam per unit length. - Use the density of concrete to find the weight. 2. **Calculate Bending Moments:** - Identify the bending moment at the center and supports. - Use beam formulas for uniformly distributed loads and point loads. 3. **Evaluate Stresses:** - Use the bending stress formula \( \sigma = \frac{M}{S} \) where M is the moment and S is the section modulus. 4. **Service Load Analysis:** - Ensure the stresses are within allowable limits provided by material properties. 5. **Load Combinations and Safety Factors:** - Consider safety factors and combination of loads as per relevant codes and standards. This example provides a basic approach to calculating the allowable service load for a beam in structural engineering. The process includes identifying loads, calculating moments and stresses, and comparing these with allowable limits based on material properties.
Transcribed Image Text:### Example: Determining the Allowable Service Load #### Problem Statement: Determine the allowable service load in the following scenario. Include beam weight. #### Diagram A: A horizontal beam is shown with a length of 20 feet, supported at both ends. The beam has a uniform load (w) applied across its length. There is also a concentrated load (Po = 2k) at the center of the beam. #### Diagram B: A triangular truss structure is illustrated with a height of 10 feet and a base of 30 feet. The truss is supported at both ends. #### Beam Specifications: - Beam moment of inertia, I - Beam section modulus, S - Concrete strength, \( f'c = 4 \) ksi - Steel yield strength, \( f_y = 50 \) ksi #### Cross-Section of Beam: - Width = 20 inches - Depth = 15 inches - Reinforcement: 4 bars of #5 rebar at the bottom (tension reinforcement) and 5 bars of #5 rebar at the top (compression reinforcement) #### Material Properties: - Concrete: \( f'c = 4 \) ksi - Steel: \( f_y = 50 \) ksi #### Calculation Steps: 1. **Determine the Self-Weight of the Beam:** - Calculate the volume of the beam per unit length. - Use the density of concrete to find the weight. 2. **Calculate Bending Moments:** - Identify the bending moment at the center and supports. - Use beam formulas for uniformly distributed loads and point loads. 3. **Evaluate Stresses:** - Use the bending stress formula \( \sigma = \frac{M}{S} \) where M is the moment and S is the section modulus. 4. **Service Load Analysis:** - Ensure the stresses are within allowable limits provided by material properties. 5. **Load Combinations and Safety Factors:** - Consider safety factors and combination of loads as per relevant codes and standards. This example provides a basic approach to calculating the allowable service load for a beam in structural engineering. The process includes identifying loads, calculating moments and stresses, and comparing these with allowable limits based on material properties.
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