quistiom 3can you use a moment of area method ### Problem 1**Objective:** Find $\Delta A$ and $\Theta B$.**Diagram Description:**- A structure with points labeled A and B.- A spring between A and a point (unlabeled) with a force of $2 \text{ kN}$.- A length of $5'$ from $A$ to $B$.- A segment of $10'$ from the spring to a fixed point on the right.- Another spring of $3'$ is attached on the right side.### Problem 2**Objective:** Find $\Delta B$ on side $B-C$, and $\Theta C$ on side $C-D$.**Diagram Description:**- A horizontal structural bar with multiple forces and points.- $3'$ between a support at the left and point B.- A force of $4 \text{ kN}$ downward at point B.- $3'$ from B to point C.- A pin at point C.- $10'$ from C to a fixed support at point D on the right.- A spring with force of $2.5 \text{ kN}$ located at the right end near D.This representation of static structures involves determining displacements ($\Delta$) and angles ($\Theta$) at specified points due to applied forces and constraints. Understanding these aspects is crucial in the field of structural engineering and mechanics.

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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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quistiom 3

can you use a moment of area method

### Problem 1
**Objective:** Find $\Delta A$ and $\Theta B$.

**Diagram Description:**
- A structure with points labeled A and B.
- A spring between A and a point (unlabeled) with a force of $2 \text{ kN}$.
- A length of $5'$ from $A$ to $B$.
- A segment of $10'$ from the spring to a fixed point on the right.
- Another spring of $3'$ is attached on the right side.

### Problem 2
**Objective:** Find $\Delta B$ on side $B-C$, and $\Theta C$ on side $C-D$.

**Diagram Description:**
- A horizontal structural bar with multiple forces and points.
- $3'$ between a support at the left and point B.
- A force of $4 \text{ kN}$ downward at point B.
- $3'$ from B to point C.
- A pin at point C.
- $10'$ from C to a fixed support at point D on the right.
- A spring with force of $2.5 \text{ kN}$ located at the right end near D.

This representation of static structures involves determining displacements ($\Delta$) and angles ($\Theta$) at specified points due to applied forces and constraints. Understanding these aspects is crucial in the field of structural engineering and mechanics.

Expert Solution

Step 1: Support reaction:

To calculate support reactions

The moment at right support = 0

$rightwards double arrow straight R subscript straight B left parenthesis 10 right parenthesis minus 2 left parenthesis 15 right parenthesis left parenthesis 15 over 2 right parenthesis plus 2 left parenthesis 3 right parenthesis left parenthesis 3 over 2 right parenthesis equals 0 space space space straight R subscript straight B equals 21.6 space Taking space the space sum space of space vertical space forces comma sum for blank of straight F subscript straight y equals 0 space rightwards double arrow straight R subscript straight B plus straight R subscript straight C minus 2 left parenthesis 18 right parenthesis equals 0 straight R subscript straight C equals 36 minus 21.6 straight R subscript straight C equals 14.4$

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