Part1,5,6 please ## Understanding Bending Stress in a Cantilever BeamThe cantilever beam shown in Figure A is subjected to load magnitudes of \( P_z = 3.3 \) kips and \( P_y = 8.1 \) kips. The flanged cross-section shown in Figure B has dimensions of \( b_f = 7.6 \) in., \( t_f = 0.64 \) in., \( d = 10.0 \) in., and \( t_w = 0.30 \) in. Using \( L = 80 \) in., determine:(a) The bending stress at point A.(b) The bending stress at point B.(c) The angle \( \beta \) for the orientation of the neutral axis relative to the \( +z \) axis. Note that positive \( \beta \) angles rotate clockwise from the \( +z \) axis.### Figure Descriptions**Figure A:** Displays a cantilever beam fixed at one end, with loads \( P_z \) and \( P_y \) acting downwards at the free end. The beam is oriented with the \( x \), \( y \), and \( z \) axes labeled, and points A and B marked along the beam length.**Figure B:** Shows the cross-section of the beam with the following labeled dimensions and axes:- \( b_f \): Flange breadth- \( t_f \): Flange thickness- \( d \): Total depth of the cross-section- \( t_w \): Web thickness- \( y \), \( z \): Axes of orientation for the cross-section### Part 1: Calculating the Area Moment of InertiaFor the cross-section, determine:- The area moment of inertia \( I_z \) about the \( z \) axis.- The area moment of inertia \( I_y \) about the \( y \) axis.\[ I_z = \quad \text{in.}^4 \]\[ I_y = \quad \text{in.}^4 \]#### Interactive Features- Enter values in provided fields to solve the problem.- Utilize the eTextbook and media resources for additional information and understanding.- Save work for later review or submit answers for evaluation.This resource serves as a practical guide for calculating bending stresses and understanding structural behavior under specific loading conditions. Part 5Determine the bending stress at \( B \). Use the sign convention for normal stresses.\[\sigma_{x, B} = \, \text{___} \, \text{ksi}\][Input Box]eTextbook and Media[Save for Later] [Submit Answer]---Part 6Determine the angle \( \beta \) for the orientation of the neutral axis relative to the \( +z \) axis. Note that positive \( \beta \) angles rotate clockwise from the \( +z \) axis.\[\beta = \, \text{___} \, ^\circ\][Input Box]eTextbook and Media[Save for Later] [Submit Answer]

Answered: Image /qna-images/answer/74f2d99d-ada9-4aef-8101-d2cfcec366f1.jpg

The cantilever beam shown in Figure A is subjected to load magnitudes o shown in Figure B has dimensions of by = 7.6 in., tf = 0.64 in., d = 10 (a) the bending stress at point A. (b) the bending stress at point B. (c) the angle for the orientation of the neutral axis relative to the + za axis. L D C by Iw. B C d

The cantilever beam shown in Figure A is subjected to load magnitudes o shown in Figure B has dimensions of by = 7.6 in., tf = 0.64 in., d = 10 (a) the bending stress at point A. (b) the bending stress at point B. (c) the angle for the orientation of the neutral axis relative to the + za axis. L D C by Iw. B C d

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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Members with compression and bending

Compression members are structural elements that carry compressive axial force. They are the vertical members of a building that support beams and their design, which is governed by buckling and strength. Columns are known as struct or compression members, which are subjected to compressive forces. These members provide stiffness to the building and avoid any imperfection regarding the transfer of axial load. For instance, webs in a truss, braces in a framed structure, tiers, and so on.

Question

Part1,5,6 please

## Understanding Bending Stress in a Cantilever Beam

The cantilever beam shown in Figure A is subjected to load magnitudes of \( P_z = 3.3 \) kips and \( P_y = 8.1 \) kips. The flanged cross-section shown in Figure B has dimensions of \( b_f = 7.6 \) in., \( t_f = 0.64 \) in., \( d = 10.0 \) in., and \( t_w = 0.30 \) in. Using \( L = 80 \) in., determine:

(a) The bending stress at point A.
(b) The bending stress at point B.
(c) The angle \( \beta \) for the orientation of the neutral axis relative to the \( +z \) axis. Note that positive \( \beta \) angles rotate clockwise from the \( +z \) axis.

### Figure Descriptions
**Figure A:** Displays a cantilever beam fixed at one end, with loads \( P_z \) and \( P_y \) acting downwards at the free end. The beam is oriented with the \( x \), \( y \), and \( z \) axes labeled, and points A and B marked along the beam length.

**Figure B:** Shows the cross-section of the beam with the following labeled dimensions and axes:
- \( b_f \): Flange breadth
- \( t_f \): Flange thickness
- \( d \): Total depth of the cross-section
- \( t_w \): Web thickness
- \( y \), \( z \): Axes of orientation for the cross-section

### Part 1: Calculating the Area Moment of Inertia
For the cross-section, determine:
- The area moment of inertia \( I_z \) about the \( z \) axis.
- The area moment of inertia \( I_y \) about the \( y \) axis.

\[ I_z = \quad \text{in.}^4 \]
\[ I_y = \quad \text{in.}^4 \]

#### Interactive Features
- Enter values in provided fields to solve the problem.
- Utilize the eTextbook and media resources for additional information and understanding.
- Save work for later review or submit answers for evaluation.

This resource serves as a practical guide for calculating bending stresses and understanding structural behavior under specific loading conditions.

Part 5

Determine the bending stress at \( B \). Use the sign convention for normal stresses.

\[
\sigma_{x, B} = \, \text{___} \, \text{ksi}
\]

[Input Box]

eTextbook and Media

[Save for Later] [Submit Answer]

---

Part 6

Determine the angle \( \beta \) for the orientation of the neutral axis relative to the \( +z \) axis. Note that positive \( \beta \) angles rotate clockwise from the \( +z \) axis.

\[
\beta = \, \text{___} \, ^\circ
\]

[Input Box]

eTextbook and Media

[Save for Later] [Submit Answer]

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