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(2) A square member (400mm x 400mm) sustains an internal shear force of 150 kN and an internal bending moment of 250 kN-m as shown. (a). What is the axis of bending? (b). What is the moment of inertia about the axis of bending? (c). Compute the stress at Point P that results from the shear force. Ans. 1.05 MPa 200 mm 100 mm 100 mm 47 150 kN POINT P 250 kN.m 200 mm -100 100 mm mm

(2) A square member (400mm x 400mm) sustains an internal shear force of 150 kN and an internal bending moment of 250 kN-m as shown. (a). What is the axis of bending? (b). What is the moment of inertia about the axis of bending? (c). Compute the stress at Point P that results from the shear force. Ans. 1.05 MPa 200 mm 100 mm 100 mm 47 150 kN POINT P 250 kN.m 200 mm -100 100 mm mm

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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## Analysis of Stresses in a Square Member ### Problem Statement A square member (400 mm x 400 mm) sustains an internal shear force of 150 kN and an internal bending moment of 250 kN-m, as shown in the diagram. ### Diagram Description The diagram illustrates a 3D view of the square member. The coordinates are marked as x, y, and z. - A shear force of 150 kN is applied, depicted by an arrow pointing along the positive y-axis. - A bending moment of 250 kN-m is applied, shown by a curved arrow around the z-axis. - Point P is marked on the member, near one side of the square cross-section. ### Questions and Answers (a) **What is the axis of bending?** - The bending is about the z-axis, as indicated by the curved arrow. (b) **What is the moment of inertia about the axis of bending?** - **Answer:** The moment of inertia is not provided directly. It would typically need to be calculated based on cross-sectional geometric properties. (c) **Compute the stress at Point P that results from the shear force.** - **Answer:** 1.05 MPa (d) **Compute the stress at Point P that results from the bending moment.** - **Answer:** 11.7 MPa (e) **Illustrate the combined state of stress at Point P on this stress cube.** - This would involve drawing the three-dimensional stress cube at Point P with the respective shear and normal stresses calculated in the previous steps. The stress cube is visually represented in the document as a 3D block aligned with the coordinate axes. This layout gives an overview of how to analyze structural members under combined loading conditions.
Transcribed Image Text:## Analysis of Stresses in a Square Member ### Problem Statement A square member (400 mm x 400 mm) sustains an internal shear force of 150 kN and an internal bending moment of 250 kN-m, as shown in the diagram. ### Diagram Description The diagram illustrates a 3D view of the square member. The coordinates are marked as x, y, and z. - A shear force of 150 kN is applied, depicted by an arrow pointing along the positive y-axis. - A bending moment of 250 kN-m is applied, shown by a curved arrow around the z-axis. - Point P is marked on the member, near one side of the square cross-section. ### Questions and Answers (a) **What is the axis of bending?** - The bending is about the z-axis, as indicated by the curved arrow. (b) **What is the moment of inertia about the axis of bending?** - **Answer:** The moment of inertia is not provided directly. It would typically need to be calculated based on cross-sectional geometric properties. (c) **Compute the stress at Point P that results from the shear force.** - **Answer:** 1.05 MPa (d) **Compute the stress at Point P that results from the bending moment.** - **Answer:** 11.7 MPa (e) **Illustrate the combined state of stress at Point P on this stress cube.** - This would involve drawing the three-dimensional stress cube at Point P with the respective shear and normal stresses calculated in the previous steps. The stress cube is visually represented in the document as a 3D block aligned with the coordinate axes. This layout gives an overview of how to analyze structural members under combined loading conditions.
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