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r= cos 8= sin 8= q/unit length 0x q/unit length 0 de P(r,0) og Ter=Tre 5. A line load of q per unit length is applied at the ground surface as shown in the Figure above with polar system: Given q = 35kN/m, calculate stresses at x =3.5 m and=2,0 m.

r= cos 8= sin 8= q/unit length 0x q/unit length 0 de P(r,0) og Ter=Tre 5. A line load of q per unit length is applied at the ground surface as shown in the Figure above with polar system: Given q = 35kN/m, calculate stresses at x =3.5 m and=2,0 m.

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 line load of \( q \) per unit length is applied at the ground surface, as shown in the figure above with a polar system. **Given:** - \( q = 35 \, \text{kN/m} \) **Task:** Calculate stresses at \( x = 3.5 \, \text{m} \) and \( z = 2.0 \, \text{m} \). ## Description of Diagrams ### Left Diagram: - **Coordinate System:** Cartesian with \( x \) and \( z \) axes. - **Variables:** - \( \theta \): Angle between the \( z \)-axis and line to point \( P \). - \( r = \sqrt{x^2 + z^2} \): Radial distance from origin to point \( P \). - \( \cos \theta = \frac{z}{\sqrt{x^2 + z^2}} \) - \( \sin \theta = \frac{x}{\sqrt{x^2 + z^2}} \) - **Stress Components:** - \( \sigma_x \): Normal stress in the x-direction. - \( \sigma_z \): Normal stress in the z-direction. - \( \tau_{xz} \): Shear stress on the plane. ### Right Diagram: - **Coordinate System:** Polar. - **Variables:** - \( \sigma_r \): Radial normal stress. - \( \sigma_\theta \): Circumferential normal stress. - \( \tau_{r\theta} \) (or \( \tau_{\theta r} \)): Shear stress in the radial-circumferential plane. - **Element:** Infinitesimal sector at angle \( \theta \). ## Calculation Instructions To solve the problem, utilize the given parameters and the stress distribution formulas for a line load applied at the surface. Compute the stresses \( \sigma_x \), \( \sigma_z \), and \( \tau_{xz} \) at the specified coordinates \( x = 3.5 \, \text{m} \) and \( z = 2.0 \, \text{m} \).
Transcribed Image Text:## Problem Statement A line load of \( q \) per unit length is applied at the ground surface, as shown in the figure above with a polar system. **Given:** - \( q = 35 \, \text{kN/m} \) **Task:** Calculate stresses at \( x = 3.5 \, \text{m} \) and \( z = 2.0 \, \text{m} \). ## Description of Diagrams ### Left Diagram: - **Coordinate System:** Cartesian with \( x \) and \( z \) axes. - **Variables:** - \( \theta \): Angle between the \( z \)-axis and line to point \( P \). - \( r = \sqrt{x^2 + z^2} \): Radial distance from origin to point \( P \). - \( \cos \theta = \frac{z}{\sqrt{x^2 + z^2}} \) - \( \sin \theta = \frac{x}{\sqrt{x^2 + z^2}} \) - **Stress Components:** - \( \sigma_x \): Normal stress in the x-direction. - \( \sigma_z \): Normal stress in the z-direction. - \( \tau_{xz} \): Shear stress on the plane. ### Right Diagram: - **Coordinate System:** Polar. - **Variables:** - \( \sigma_r \): Radial normal stress. - \( \sigma_\theta \): Circumferential normal stress. - \( \tau_{r\theta} \) (or \( \tau_{\theta r} \)): Shear stress in the radial-circumferential plane. - **Element:** Infinitesimal sector at angle \( \theta \). ## Calculation Instructions To solve the problem, utilize the given parameters and the stress distribution formulas for a line load applied at the surface. Compute the stresses \( \sigma_x \), \( \sigma_z \), and \( \tau_{xz} \) at the specified coordinates \( x = 3.5 \, \text{m} \) and \( z = 2.0 \, \text{m} \).
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Step 1: Introduction

A line load q per unit length is applied at the ground surface which is shown in the above figure. 

q = 35 kN/m 

We have to find out the stress at x = 3.5 m and z= 2m. 

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