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QUESTION 1 Find the most economical W14 for a beam with a span of 30' and a uniform load of 4k/f and point loads every 6ft of 10k. Fv 20ksi, Fb 30ksi and E = 29,000ksi, and Aall - L/240.

QUESTION 1 Find the most economical W14 for a beam with a span of 30' and a uniform load of 4k/f and point loads every 6ft of 10k. Fv 20ksi, Fb 30ksi and E = 29,000ksi, and Aall - L/240.

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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### Question 1 **Problem Statement:** Find the most economical W14 for a beam with a span of 30’ and a uniform load of 4k/f and point loads every 6ft of 10k. The given parameters are: - \( F_v = 20 \text{ ksi} \) - \( F_b = 30 \text{ ksi} \) - \( E = 29,000 \text{ ksi} \) - \( \Delta_{\text{all}} = L/240 \) **Explanation:** This problem involves the selection of an appropriate steel section (W14) for a beam subjected to both uniform and point loads. The constraints provided include the allowable shear stress (\( F_v \)), the allowable bending stress (\( F_b \)), modulus of elasticity (\( E \)), and the allowable deflection (\( \Delta_{\text{all}} \)). The key steps to solve this problem are: 1. **Calculate Shear Force:** - Determine the maximum shear force exerted on the beam due to the uniform load and the point loads. 2. **Determine Bending Moment:** - Calculate the maximum bending moment considering the loads and the span length. 3. **Select Section Modulus:** - Use the bending stress formula to find the required section modulus. 4. **Check for Deflection:** - Ensure that the chosen beam section satisfies the deflection criteria. By carrying out these calculations, the goal is to find the most economical (lightest) W14 section that can safely support the applied loads without exceeding the permissible stresses and deflection limits.
Transcribed Image Text:### Question 1 **Problem Statement:** Find the most economical W14 for a beam with a span of 30’ and a uniform load of 4k/f and point loads every 6ft of 10k. The given parameters are: - \( F_v = 20 \text{ ksi} \) - \( F_b = 30 \text{ ksi} \) - \( E = 29,000 \text{ ksi} \) - \( \Delta_{\text{all}} = L/240 \) **Explanation:** This problem involves the selection of an appropriate steel section (W14) for a beam subjected to both uniform and point loads. The constraints provided include the allowable shear stress (\( F_v \)), the allowable bending stress (\( F_b \)), modulus of elasticity (\( E \)), and the allowable deflection (\( \Delta_{\text{all}} \)). The key steps to solve this problem are: 1. **Calculate Shear Force:** - Determine the maximum shear force exerted on the beam due to the uniform load and the point loads. 2. **Determine Bending Moment:** - Calculate the maximum bending moment considering the loads and the span length. 3. **Select Section Modulus:** - Use the bending stress formula to find the required section modulus. 4. **Check for Deflection:** - Ensure that the chosen beam section satisfies the deflection criteria. By carrying out these calculations, the goal is to find the most economical (lightest) W14 section that can safely support the applied loads without exceeding the permissible stresses and deflection limits.
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