### Transcription for Educational Website#### Stress Transformation ProblemThe problem is about determining the stress state on a rotated element. **Context:**- **Stress State:** The stress at a point in a member is depicted on a rectangular stress element.- **Figure Reference:** Figure 6 shows the stress configuration.- **Given Stresses:** - \(|\sigma_x| = 31 \text{ ksi}\) - \(|\sigma_y| = 38 \text{ ksi}\)**Task:**- Determine the stress state \((\sigma_x', \sigma_y', \tau_x'y')\) on an element rotated such that the \(+\text{x}'\) axis is 30° below the \(-\text{x}\) axis of the original stress element.- Provide your answers rounded to three significant figures, separated by commas.**Input Box:**- Answers should be entered in the format: \(\sigma_x', \sigma_y', \tau_x'y'\) (in ksi).#### Figure DescriptionThe accompanying figure illustrates a square element experiencing stresses, with:- \(\sigma_x\) shown as a horizontal arrow pointing outward from the right face.- \(\sigma_y\) shown as a vertical arrow pointing outward from the top face.- These arrows indicate the directions and relative magnitudes of the applied stresses on the element. ### Instructions1. Understand the given stress conditions.2. Use stress transformation equations to compute the rotated stresses.3. Input your answers in the provided format and submit.### Additional Resources- [View Available Hint(s)](link to hints) for guidance on solving the problem.

So angle is clockwise and θ=-30°σx=31ksiσy=-38ksiτxy=0Using Transformation of stresses equations:σx'=σx+σy2+σx-σy2cos2θ+τxysin2θσx'=31-382+31+382cos2(-30)+0sin2(-30)σx'=13.75ksiσy'=σx+σy2-σx-σy2cos2θ-τxysin2θσy'=31-382-31+382cos2(-30)-0sin2(-30)σy'=-20.75ksiτx'y'=-31+382sin2(-30)-0cos2(-30)τx'y'=29.88ksi

Engineering

Civil Engineering

The state of stress at a point in a member is shown on the rectangular stress element in (Eigure 6) where the magnitudes of the stresses are l0z| = 31 ksi and lo, = 38 ksi. Determine the state of stress on an element rotated such that the +z' axis is 30° below the -z axis of the original stress element. Express your answers, separated by commas, to three significant figures. View Available Hint/s)

The state of stress at a point in a member is shown on the rectangular stress element in (Eigure 6) where the magnitudes of the stresses are l0z| = 31 ksi and lo, = 38 ksi. Determine the state of stress on an element rotated such that the +z' axis is 30° below the -z axis of the original stress element. Express your answers, separated by commas, to three significant figures. View Available Hint/s)

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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Concept explainers

Solid Mechanics

Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.

Question

### Transcription for Educational Website

#### Stress Transformation Problem

The problem is about determining the stress state on a rotated element.

**Context:**
- **Stress State:** The stress at a point in a member is depicted on a rectangular stress element.
- **Figure Reference:** Figure 6 shows the stress configuration.
- **Given Stresses:**
- \(|\sigma_x| = 31 \text{ ksi}\)
- \(|\sigma_y| = 38 \text{ ksi}\)

**Task:**
- Determine the stress state \((\sigma_x', \sigma_y', \tau_x'y')\) on an element rotated such that the \(+\text{x}'\) axis is 30° below the \(-\text{x}\) axis of the original stress element.
- Provide your answers rounded to three significant figures, separated by commas.

**Input Box:**
- Answers should be entered in the format: \(\sigma_x', \sigma_y', \tau_x'y'\) (in ksi).

#### Figure Description

The accompanying figure illustrates a square element experiencing stresses, with:
- \(\sigma_x\) shown as a horizontal arrow pointing outward from the right face.
- \(\sigma_y\) shown as a vertical arrow pointing outward from the top face.
- These arrows indicate the directions and relative magnitudes of the applied stresses on the element.

### Instructions
1. Understand the given stress conditions.
2. Use stress transformation equations to compute the rotated stresses.
3. Input your answers in the provided format and submit.

### Additional Resources
- [View Available Hint(s)](link to hints) for guidance on solving the problem.

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Thanks for the help
Mohr’s circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 600 psi in size. (a) Determine the stresses σx, σy, and the magnitude of τxy and show them on a stress element. (b) Determine the principal stresses and the magnitude of the maximum in-plane shear stress acting at the point and show these stresses on an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16).
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