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A W14x90 is used as a simply supported, uniformly loaded beam with a span length of 40 feet and continuous lateral support. The yield stress, Fy, is 50 ksi. If the ratio of live load to dead load is 2.5, compute the available strength and determine the maximum total service load, in kips/ft, that can be supported. (Hint: This is not a compact shape!)

A W14x90 is used as a simply supported, uniformly loaded beam with a span length of 40 feet and continuous lateral support. The yield stress, Fy, is 50 ksi. If the ratio of live load to dead load is 2.5, compute the available strength and determine the maximum total service load, in kips/ft, that can be supported. (Hint: This is not a compact shape!)

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 Statement:** A W14×90 is used as a simply supported, uniformly loaded beam with a span length of 40 feet and continuous lateral support. The yield stress, \(F_y\), is 50 ksi. If the ratio of live load to dead load is 2.5, compute the available strength and determine the maximum total service load, in kips/ft, that can be supported. (Hint: This is not a compact shape!) **Explanation:** This problem involves determining the maximum load that a given beam can support under specified conditions. Here’s a breakdown of the given details and the steps involved: 1. **Beam Details:** - **Type:** W14×90 (A wide-flange beam). - **Span Length:** 40 feet. - **Load Type:** Uniformly loaded. - **Lateral Support:** Continuous. 2. **Material Property:** - **Yield Stress (Fy):** 50 ksi (kilo-pounds per square inch). 3. **Load Ratio:** - **Live Load to Dead Load Ratio:** 2.5. 4. **Hint:** - The beam is specified to be "not a compact shape," suggesting buckling considerations or other factors may affect its design capacity. **Steps to Solve:** 1. **Determine the Section Properties:** - Find the properties of the W14×90 section from a steel handbook or database (e.g., the moment of inertia, section modulus, radius of gyration, etc.). 2. **Calculate the Bending Strength (Available Strength):** - Use the yield stress and section properties to calculate the nominal moment capacity of the beam. 3. **Account for Load Combinations:** - Apply the live-to-dead load ratio to determine the total uniform load. 4. **Determine the Service Load Capacity:** - Convert the moment capacity into a service load capacity in terms of kips/ft (considering the span length and uniformly distributed load). 5. **Apply Design Factors:** - Consider any reduction factors or safety factors as per relevant design codes or standards. This process will help to ensure the beam's design adheres to structural engineering standards, providing safe and reliable support for the specified loads. This detailed approach is essential in education to demonstrate the step-by-step procedure of solving structural engineering problems, ensuring clarity and accuracy in application and theory.
Transcribed Image Text:**Problem Statement:** A W14×90 is used as a simply supported, uniformly loaded beam with a span length of 40 feet and continuous lateral support. The yield stress, \(F_y\), is 50 ksi. If the ratio of live load to dead load is 2.5, compute the available strength and determine the maximum total service load, in kips/ft, that can be supported. (Hint: This is not a compact shape!) **Explanation:** This problem involves determining the maximum load that a given beam can support under specified conditions. Here’s a breakdown of the given details and the steps involved: 1. **Beam Details:** - **Type:** W14×90 (A wide-flange beam). - **Span Length:** 40 feet. - **Load Type:** Uniformly loaded. - **Lateral Support:** Continuous. 2. **Material Property:** - **Yield Stress (Fy):** 50 ksi (kilo-pounds per square inch). 3. **Load Ratio:** - **Live Load to Dead Load Ratio:** 2.5. 4. **Hint:** - The beam is specified to be "not a compact shape," suggesting buckling considerations or other factors may affect its design capacity. **Steps to Solve:** 1. **Determine the Section Properties:** - Find the properties of the W14×90 section from a steel handbook or database (e.g., the moment of inertia, section modulus, radius of gyration, etc.). 2. **Calculate the Bending Strength (Available Strength):** - Use the yield stress and section properties to calculate the nominal moment capacity of the beam. 3. **Account for Load Combinations:** - Apply the live-to-dead load ratio to determine the total uniform load. 4. **Determine the Service Load Capacity:** - Convert the moment capacity into a service load capacity in terms of kips/ft (considering the span length and uniformly distributed load). 5. **Apply Design Factors:** - Consider any reduction factors or safety factors as per relevant design codes or standards. This process will help to ensure the beam's design adheres to structural engineering standards, providing safe and reliable support for the specified loads. This detailed approach is essential in education to demonstrate the step-by-step procedure of solving structural engineering problems, ensuring clarity and accuracy in application and theory.
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