Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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Transcribed Image Text:### Solving for the Resultant Force in a Parallel Force System
In this problem, we will determine the resultant force, along with its magnitude and location, for a given parallel force system.
### Problem Description
The figure provided illustrates a simply supported beam with two point loads and a uniformly distributed load. The beam has supports at points \( A \) and \( B \).
The forces acting on the beam are as follows:
1. A concentrated load of 3 kips located 3 ft from the support at \( A \).
2. A concentrated load of 10 kips located 7 ft from the support at \( A \).
3. A uniformly distributed load of 2 kips/ft acting over a span of 6 ft starting 13 ft from the support at \( A \).
### Force Diagram Explanation
- **Support Points**:
- \( A \): Pin support.
- \( B \): Roller support, located 12 feet from the pin support at \( A \).
- **Loads**:
- **3 kips Load**: Applied vertically downward, located 3 ft from point \( A \).
- **10 kips Load**: Applied vertically downward, located 7 ft from point \( A \).
- **Uniform Load**: Distributed load of 2 kips/ft over a span of 6 ft, starting 13 ft from point \( A \).
### Steps to Solve the Problem
1. **Calculate the Resultant (Magnitude) of the Forces**:
- Sum the concentrated loads.
- Determine the equivalent point load for the uniformly distributed load.
2. **Determine the Position (Location \( x \)) of the Resultant Force**:
- Calculate the moment of each force about point \( A \).
- Compute the resultant moment using the principle of moments.
### Solving for the Magnitude of the Resultant Force
- **Resultant Force from Concentrated Loads**:
\( F_{\text{resultant}} = 3 \text{ kips} + 10 \text{ kips} = 13 \text{ kips} \)
- **Resultant Force from Uniformly Distributed Load**:
\( F_{\text{uniform}} = 2 \text{ kips/ft} \times 6 \text{ ft} = 12 \text{ kips} \)
- **Total Resultant Force**:
\(
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- A r (0) 2m + d 300N 8 B 3m 307 M-1500Nm For the above diagram, given that F₁ = 800 N, w = 400 N/m and d = 4 m, calculate the following (neglect the depth of the beam). Note that there is a pin support at A and a roller support at B. Given: • The magnitude of the resultant of the applied forces, FR = 1.837 KN • The angle of the resultant forces, FR measured counter-clockwise from the negative x axis = 77.423 deg. The resultant forces, FR so that it is equivalent to the system of applied forces = 5.765 m Questions: 1. The magnitude of the reaction forces, RAX. Please provide the answer in Newtons and report to three significant figures. 2. The magnitude of the reaction forces, Ray. Please provide the answer in Newtons and report to three significant figures. 3. The magnitude of the reaction forces, Rex. Please provide the answer in Newtons and report to three significant figures. 4. The magnitude of the reaction forces, Rgy. Please provide the answer in kilo Newtons and report to three…arrow_forwardFor the beam presented below:a) What is the degree of indeterminacy; b) Determine the moment reactions at the supports and draw the shear and momentdiagrams. (Solve by expressing the internal moment in terms of vertical reactionsat A and B, EI is constant). c) What would the shear diagram look like if a transverse load P was applied right atthe middle of the beam (Make a sketch of the new shear diagram). W (30kN/m) , L (1.9m)arrow_forwardDetermine angular velocity of the bar, [rad/s], when it goes through horizontal position? The bar, WA= 100 [lb] and L=3 [ft], shown in figure is initially in the vertical position. The bar is subjected to a couple moment of M=20 [lb-ft] and a force F=50 [lb], which is always perpendicular to the end of bar. Also, the spring is attached to bar at distance L/2 from point A, and has unstretched length of lo=1.2 [ft]. The spring remains in horizontal position throughout the motion due to the roller guide at B. Determine angular velocity of the bar, o [rad/s], when it goes through horizontal position. Spring constant is k=7 [lb/ft]. Distance between point A and vertical guide is d=1.5 [ft]. F g B thing M A d ≈arrow_forward
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