**Title: Analyzing Loads in Truss Members****Introduction:**In this exercise, we will examine the forces in a truss system involving two members, \( BA \) and \( BC \). A downward load \( P \) of 250 N is applied at point \( B \). The challenge is to calculate the magnitudes of the loads supported by members \( BA \) and \( BC \).**Problem Statement:**A load \( P = 250 \, \text{N} \) is applied downward at point \( B \). It is supported by two truss members:- Member \( BA \) forms an angle \( \theta_1 = 35^\circ \) with the horizontal axis.- Member \( BC \) forms an angle \( \theta_2 = 55^\circ \) with the vertical axis.**Objective:**Calculate the magnitudes of the forces in members \( BA \) and \( BC \).**Diagram Explanation:**The diagram displays a triangular truss system:- **Point \( A \)** is at the base where member \( BA \) is anchored.- **Point \( B \)** is where the load \( P \) is applied.- **Point \( C \)** is the top end where member \( BC \) is anchored vertically.The load \( P \) acts vertically downward at point \( B \). The members \( BA \) and \( BC \) support this applied load.**Parameters:**| Parameter | Value | Units ||-----------|-------|-------|| \( P \) | 250 | N || \( \theta_1 \) | 35 | \( ^\circ \) || \( \theta_2 \) | 55 | \( ^\circ \) |**Tasks:**Calculate:1. The magnitude of the force vector along \( BA \).2. The magnitude of the force vector along \( BC \).Use static equilibrium equations and trigonometric relations to find the solutions. ### Analyzing Forces in a Structural SystemIn this exercise, we will analyze the forces in a structural system with two members, \( BA \) and \( BC \). The goal is to calculate the magnitudes of the loads supported by each member.#### Problem StatementA force \( P \) of 250 N is applied at point \( B \). Member \( BA \) makes an angle of \( \theta_1 = 35^\circ \) with the horizontal axis, while member \( BC \) makes an angle of \( \theta_2 = 55^\circ \) with the vertical axis. Determine the force vectors along members \( BA \) and \( BC \).#### Diagram Description- **Structural Members**: The diagram shows two connected members, \( BA \) and \( BC \), forming a triangular configuration.- **Angles**: - \( \theta_1 \) (35°) is the angle between member \( BA \) and the horizontal. - \( \theta_2 \) (55°) is the angle between member \( BC \) and the vertical.- **Force Application**: A downward force (P = 250 N) is applied at point \( B \).#### Parameters and Units| Parameter | Value | Units ||-----------|-------|-------|| \( P \) | 250 | N || \( \theta_1 \) | 35 | ° || \( \theta_2 \) | 55 | ° |#### CalculationsTo determine the magnitudes of the force vectors:- **Magnitude along \( BA \)**: \[ \_\_\_ \, \text{N} \]- **Magnitude along \( BC \)**: \[ \_\_\_ \, \text{N} \]These values can be found using trigonometric relationships inherent in the described angles and forces.This exercise is a fundamental problem in analyzing static structures, often encountered in fields such as civil and mechanical engineering. Understanding the force distribution provides insight into material selection and structural integrity.

Answered: Image /qna-images/answer/96174067-f499-4b6a-8c34-fae1948a7a5c.jpg

of 0₁ = 35° from horizontal and member BC at an angle of 02 = 55° from vertical. Calculate the magnitudes of the loa supported by members BA and BC. 080 2021 Caly Zupke B P parameter P 0₁ 0₂ 0₁ value units 250 N 35 55 C 0₂ A The magnitude of the force vector along BA is N The magnitude of the force vector along BC is N;

of 0₁ = 35° from horizontal and member BC at an angle of 02 = 55° from vertical. Calculate the magnitudes of the loa supported by members BA and BC. 080 2021 Caly Zupke B P parameter P 0₁ 0₂ 0₁ value units 250 N 35 55 C 0₂ A The magnitude of the force vector along BA is N The magnitude of the force vector along BC is N;

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

System of Forces

A force is an external influence or agent that changes the state of a system. According to Newton's second law, the force applied to a body is proportional to the change in momentum of a body. Hence, whenever a force is applied to a body, its momentum changes. If the body is at rest, under the action of force, its state of rest changes to motion. In other words, the magnitude of the momentum of the body changes from zero to a measurable value. Similarly, if the body possesses some initial velocity, it has some associated momentum, the effect of force can cause the body to halt or come to rest, that is, the momentum reduces to zero.

Question

**Title: Analyzing Loads in Truss Members**

**Introduction:**
In this exercise, we will examine the forces in a truss system involving two members, \( BA \) and \( BC \). A downward load \( P \) of 250 N is applied at point \( B \). The challenge is to calculate the magnitudes of the loads supported by members \( BA \) and \( BC \).

**Problem Statement:**
A load \( P = 250 \, \text{N} \) is applied downward at point \( B \). It is supported by two truss members:
- Member \( BA \) forms an angle \( \theta_1 = 35^\circ \) with the horizontal axis.
- Member \( BC \) forms an angle \( \theta_2 = 55^\circ \) with the vertical axis.

**Objective:**
Calculate the magnitudes of the forces in members \( BA \) and \( BC \).

**Diagram Explanation:**
The diagram displays a triangular truss system:
- **Point \( A \)** is at the base where member \( BA \) is anchored.
- **Point \( B \)** is where the load \( P \) is applied.
- **Point \( C \)** is the top end where member \( BC \) is anchored vertically.

The load \( P \) acts vertically downward at point \( B \). The members \( BA \) and \( BC \) support this applied load.

**Parameters:**

| Parameter | Value | Units |
|-----------|-------|-------|
| \( P \) | 250 | N |
| \( \theta_1 \) | 35 | \( ^\circ \) |
| \( \theta_2 \) | 55 | \( ^\circ \) |

**Tasks:**
Calculate:
1. The magnitude of the force vector along \( BA \).
2. The magnitude of the force vector along \( BC \).

Use static equilibrium equations and trigonometric relations to find the solutions.

### Analyzing Forces in a Structural System

In this exercise, we will analyze the forces in a structural system with two members, \( BA \) and \( BC \). The goal is to calculate the magnitudes of the loads supported by each member.

#### Problem Statement

A force \( P \) of 250 N is applied at point \( B \). Member \( BA \) makes an angle of \( \theta_1 = 35^\circ \) with the horizontal axis, while member \( BC \) makes an angle of \( \theta_2 = 55^\circ \) with the vertical axis. Determine the force vectors along members \( BA \) and \( BC \).

#### Diagram Description

- **Structural Members**: The diagram shows two connected members, \( BA \) and \( BC \), forming a triangular configuration.
- **Angles**:
- \( \theta_1 \) (35°) is the angle between member \( BA \) and the horizontal.
- \( \theta_2 \) (55°) is the angle between member \( BC \) and the vertical.
- **Force Application**: A downward force (P = 250 N) is applied at point \( B \).

#### Parameters and Units

| Parameter | Value | Units |
|-----------|-------|-------|
| \( P \) | 250 | N |
| \( \theta_1 \) | 35 | ° |
| \( \theta_2 \) | 55 | ° |

#### Calculations

To determine the magnitudes of the force vectors:

- **Magnitude along \( BA \)**: \[ \_\_\_ \, \text{N} \]

- **Magnitude along \( BC \)**: \[ \_\_\_ \, \text{N} \]

These values can be found using trigonometric relationships inherent in the described angles and forces.

This exercise is a fundamental problem in analyzing static structures, often encountered in fields such as civil and mechanical engineering. Understanding the force distribution provides insight into material selection and structural integrity.

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