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Problem 1: Determine the allowable service live load, PL assume the dead load is due to the beam weight fc = 3 ksi, fy = 60 ksi, Dc = 150 pcf. 25" 5" 4-#8 10" 10" PL 10" PL 10"

Problem 1: Determine the allowable service live load, PL assume the dead load is due to the beam weight fc = 3 ksi, fy = 60 ksi, Dc = 150 pcf. 25" 5" 4-#8 10" 10" PL 10" PL 10"

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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### Problem 1: Determining the Allowable Service Live Load (P_L) **Objective:** Determine the allowable service live load \( P_L \). Assume the dead load is due to the beam weight. **Given Data:** - Compressive strength of concrete, \( f'_c = 3 \) ksi - Yield strength of steel, \( f_y = 60 \) ksi - Density of concrete, \( D_c = 150 \) pcf **Diagrams and Measurements:** 1. **Cross-Section View of Beam:** - **Height:** 25 inches - **Width:** 10 inches - **Bottom Cover Thickness:** 5 inches - **Reinforcement:** 4 #8 bars (4-#8) 2. **Simply Supported Beam with Point Loads:** - **Beam Length:** 30 inches - **Point Loads:** 2 point loads \( P_L \) each at intervals of 10 inches **Diagram Explanation:** - The left diagram shows the cross-section of a rectangular beam, with reinforcement consisting of four number 8 bars (commonly denoted as 4-#8). The cross-section has a total height of 25 inches and a width of 10 inches, with a 5-inch cover at the bottom. - The right diagram shows the side view of a simply supported beam subjected to two point loads \( P_L \). The beam has a total span of 30 inches, with point loads placed 10 inches apart along its length. **Analysis Steps:** 1. **Calculate Dead Load of the Beam:** The dead load can be computed based on the density of the concrete and the dimensions of the beam cross-section. 2. **Determine Moment Capacity:** Using the material properties \( f'_c \) and \( f_y \), calculate the moment capacity of the beam section reinforced with 4 #8 bars. 3. **Calculate Allowable Live Load \( P_L \):** With the dead load known and structural analysis, determine the maximum allowable live load \( P_L \) that can be safely applied without exceeding the capacity of the beam. By following these steps, you can determine the allowable live load for this structural element, ensuring that the design is safe and efficient for its intended application.
Transcribed Image Text:### Problem 1: Determining the Allowable Service Live Load (P_L) **Objective:** Determine the allowable service live load \( P_L \). Assume the dead load is due to the beam weight. **Given Data:** - Compressive strength of concrete, \( f'_c = 3 \) ksi - Yield strength of steel, \( f_y = 60 \) ksi - Density of concrete, \( D_c = 150 \) pcf **Diagrams and Measurements:** 1. **Cross-Section View of Beam:** - **Height:** 25 inches - **Width:** 10 inches - **Bottom Cover Thickness:** 5 inches - **Reinforcement:** 4 #8 bars (4-#8) 2. **Simply Supported Beam with Point Loads:** - **Beam Length:** 30 inches - **Point Loads:** 2 point loads \( P_L \) each at intervals of 10 inches **Diagram Explanation:** - The left diagram shows the cross-section of a rectangular beam, with reinforcement consisting of four number 8 bars (commonly denoted as 4-#8). The cross-section has a total height of 25 inches and a width of 10 inches, with a 5-inch cover at the bottom. - The right diagram shows the side view of a simply supported beam subjected to two point loads \( P_L \). The beam has a total span of 30 inches, with point loads placed 10 inches apart along its length. **Analysis Steps:** 1. **Calculate Dead Load of the Beam:** The dead load can be computed based on the density of the concrete and the dimensions of the beam cross-section. 2. **Determine Moment Capacity:** Using the material properties \( f'_c \) and \( f_y \), calculate the moment capacity of the beam section reinforced with 4 #8 bars. 3. **Calculate Allowable Live Load \( P_L \):** With the dead load known and structural analysis, determine the maximum allowable live load \( P_L \) that can be safely applied without exceeding the capacity of the beam. By following these steps, you can determine the allowable live load for this structural element, ensuring that the design is safe and efficient for its intended application.
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