### Spring-Mass System AnalysisThe beam of negligible weight is supported by springs at points A and B. Spring A has a spring constant of \( k_1 = 800 \, \text{N/m} \), and spring B has a spring constant of \( k_2 = 1550 \, \text{N/m} \). Assume the beam is horizontal and springs are unstretched when the distributed load is removed.#### Diagram Explanation1. **Top Diagram:** - It shows a horizontal beam supported by two springs labeled \( k_1 \) (at point A) and \( k_2 \) (at point B). - A triangular distributed load \( W_1 \) is applied along the beam, starting from point A to the right. - The beam is divided into two sections: \( d_1 = 2 \, \text{m} \) and \( d_2 = 2.5 \, \text{m} \).2. **Bottom Diagram:** - Displays the effect of the load causing the beam to tilt at an angle \( \theta_1 \). - The beam slants, showing the effect of the differential spring constants and the distributed load.#### Given Values- \( d_1 = 2 \, \text{m} \)- \( d_2 = 2.5 \, \text{m} \)- \( W_1 = 600 \, \text{N/m} \)#### Problems to Solvea. Determine the magnitude of the force in spring A, \( F_A \).b. Determine the magnitude of the force in spring B, \( F_B \).c. Determine the stretch in spring A, \( s_A \).---This exercise demonstrates the analysis of springs in a practical system, integrating concepts of mechanics and elasticity. The diagram illustrates a beam suspended by two springs at points A and B, creating an inclined plane with an angle \( \theta_1 \). The beam is not necessarily to scale, but the values associated with the setup are provided in the table below.**Values for the Figure**| Variable | Value ||----------|------------|| \( d_1 \) | 2 m || \( d_2 \) | 2.5 m || \( W_1 \) | 600 N/m |**Tasks**a. Determine the magnitude of the force in spring A, \( F_A \).b. Determine the magnitude of the force in spring B, \( F_B \). c. Determine the stretch in spring A, \( s_A \).d. Determine the stretch in spring B, \( s_B \).e. Determine the angle of tilt of the beam, \( \theta_1 \).Ensure to round your final answers to 3 significant digits/figures.**Solutions**1. \( F_A = \_\_\_\_\_ \) N2. \( F_B = \_\_\_\_\_ \) N3. \( s_A = \_\_\_\_\_ \) m4. \( s_B = \_\_\_\_\_ \) m5. \( \theta_1 = \_\_\_\_\_ \) degrees

Given data - d1 = 2 m d2 = 2.5 m W = 600 N/m K1 = 800 N/m K2 = 1550 N/m Find out - a. Determine the…

The beam of negligible weight is supported by springs at point A and B. Spring A has a spring constant of k₁= 800 -, and N m N Assume the spring B has a spring constant of k₂= 1550 beam is horizontal and springs are unstretched when the distributed load is removed. k1 d1 W₁ d2 m K2 B B

The beam of negligible weight is supported by springs at point A and B. Spring A has a spring constant of k₁= 800 -, and N m N Assume the spring B has a spring constant of k₂= 1550 beam is horizontal and springs are unstretched when the distributed load is removed. k1 d1 W₁ d2 m K2 B B

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

### Spring-Mass System Analysis

The beam of negligible weight is supported by springs at points A and B. Spring A has a spring constant of \( k_1 = 800 \, \text{N/m} \), and spring B has a spring constant of \( k_2 = 1550 \, \text{N/m} \). Assume the beam is horizontal and springs are unstretched when the distributed load is removed.

#### Diagram Explanation

1. **Top Diagram:**
- It shows a horizontal beam supported by two springs labeled \( k_1 \) (at point A) and \( k_2 \) (at point B).
- A triangular distributed load \( W_1 \) is applied along the beam, starting from point A to the right.
- The beam is divided into two sections: \( d_1 = 2 \, \text{m} \) and \( d_2 = 2.5 \, \text{m} \).

2. **Bottom Diagram:**
- Displays the effect of the load causing the beam to tilt at an angle \( \theta_1 \).
- The beam slants, showing the effect of the differential spring constants and the distributed load.

#### Given Values

- \( d_1 = 2 \, \text{m} \)
- \( d_2 = 2.5 \, \text{m} \)
- \( W_1 = 600 \, \text{N/m} \)

#### Problems to Solve

a. Determine the magnitude of the force in spring A, \( F_A \).

b. Determine the magnitude of the force in spring B, \( F_B \).

c. Determine the stretch in spring A, \( s_A \).

---

This exercise demonstrates the analysis of springs in a practical system, integrating concepts of mechanics and elasticity.

The diagram illustrates a beam suspended by two springs at points A and B, creating an inclined plane with an angle \( \theta_1 \). The beam is not necessarily to scale, but the values associated with the setup are provided in the table below.

**Values for the Figure**

| Variable | Value |
|----------|------------|
| \( d_1 \) | 2 m |
| \( d_2 \) | 2.5 m |
| \( W_1 \) | 600 N/m |

**Tasks**

a. Determine the magnitude of the force in spring A, \( F_A \).

b. Determine the magnitude of the force in spring B, \( F_B \).

c. Determine the stretch in spring A, \( s_A \).

d. Determine the stretch in spring B, \( s_B \).

e. Determine the angle of tilt of the beam, \( \theta_1 \).

Ensure to round your final answers to 3 significant digits/figures.

**Solutions**

1. \( F_A = \_\_\_\_\_ \) N

2. \( F_B = \_\_\_\_\_ \) N

3. \( s_A = \_\_\_\_\_ \) m

4. \( s_B = \_\_\_\_\_ \) m

5. \( \theta_1 = \_\_\_\_\_ \) degrees

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