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14–6. Determine the vertical deflection of joint O and the force in member 2 of the truss in Prob. 14–5. 4 ft 3 ft 2k 18 4 ft- Probs. 14-5/6

14–6. Determine the vertical deflection of joint O and the force in member 2 of the truss in Prob. 14–5. 4 ft 3 ft 2k 18 4 ft- Probs. 14-5/6

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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14-6

**Problems 14-5/6** **14-5.** Determine the stiffness matrix \( \mathbf{K} \) for the truss. Given: - Cross-sectional area \( A = 0.75 \, \text{in}^2 \) - Modulus of elasticity \( E = 29 \times 10^3 \, \text{ksi} \) Assume all joints are pin connected. **14-6.** Determine the vertical deflection of joint \( \mathsf{1} \) and the force in member \( 2 \) of the truss in Problem 14-5. **Diagram Explanation:** The diagram depicts a 2D truss structure consisting of three main inclined members forming two triangles with a vertical and horizontal bracing. The truss is supported at joints labeled \( ③ \) and \( ④ \), with members numbered from \( 1 \) to \( 6 \). - **Points and Angles**: The points \( ①, ②, ③, \) and \( ④ \) represent joints. The horizontal members (bottom) are connected to joint \( ④ \) and slant upwards towards joint \( ① \), forming acute angles at joints \( ④ \) and \( ① \). - **Dimensions**: The height of the triangle on the left is noted as 4 ft, and the horizontal base measures 4 ft. Joint \( ① \) is positioned 2 ft horizontally from the left-hand side. - **Loads**: There is an upward force of 2 kips applied at joint \( ① \) in the downward direction and an inward arrow at the bottom of joint \( ④ \), suggesting reaction forces. - **Member Forces and Directions**: Members are numbered and shown with directions of stress (compression or tension) as indicated by arrows: - Member \( ② \) forming the upper inclined section. - Member \( ③ \) is vertical. - Other members form the triangular and supporting structure. This truss is a standard example used in structural analysis to illustrate the calculation of internal member forces and joint deflections when subjected to specific loads.
Transcribed Image Text:**Problems 14-5/6** **14-5.** Determine the stiffness matrix \( \mathbf{K} \) for the truss. Given: - Cross-sectional area \( A = 0.75 \, \text{in}^2 \) - Modulus of elasticity \( E = 29 \times 10^3 \, \text{ksi} \) Assume all joints are pin connected. **14-6.** Determine the vertical deflection of joint \( \mathsf{1} \) and the force in member \( 2 \) of the truss in Problem 14-5. **Diagram Explanation:** The diagram depicts a 2D truss structure consisting of three main inclined members forming two triangles with a vertical and horizontal bracing. The truss is supported at joints labeled \( ③ \) and \( ④ \), with members numbered from \( 1 \) to \( 6 \). - **Points and Angles**: The points \( ①, ②, ③, \) and \( ④ \) represent joints. The horizontal members (bottom) are connected to joint \( ④ \) and slant upwards towards joint \( ① \), forming acute angles at joints \( ④ \) and \( ① \). - **Dimensions**: The height of the triangle on the left is noted as 4 ft, and the horizontal base measures 4 ft. Joint \( ① \) is positioned 2 ft horizontally from the left-hand side. - **Loads**: There is an upward force of 2 kips applied at joint \( ① \) in the downward direction and an inward arrow at the bottom of joint \( ④ \), suggesting reaction forces. - **Member Forces and Directions**: Members are numbered and shown with directions of stress (compression or tension) as indicated by arrows: - Member \( ② \) forming the upper inclined section. - Member \( ③ \) is vertical. - Other members form the triangular and supporting structure. This truss is a standard example used in structural analysis to illustrate the calculation of internal member forces and joint deflections when subjected to specific loads.
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