### Problem 3/99#### Problem Statement:The uniform 15-kg plate is welded to the vertical shaft, which is supported by bearings A and B. Calculate the magnitude of the force supported by bearing B during application of the 120-N·m couple to the shaft. The cable from C to D prevents the plate and shaft from turning, and the weight of the assembly is carried entirely by bearing A.#### Diagram Explanation:The provided diagram illustrates the structural setup for the problem. Below is a detailed explanation of the diagram:1. **Vertical Shaft and Plate**: - A vertical shaft passes through and supports a horizontally oriented plate. - The plate is denoted by points C and D, with C on the left and D on the right. 2. **Bearings**: - There are two bearings labeled as points A and B. - Bearing A is located at the upper part of the shaft, 200 mm down from the top. - Bearing B is positioned 80 mm below bearing A, making it 280 mm down from the top of the shaft. 3. **Couple**: - A twisting couple of 120 N·m is applied to the top of the shaft. This couple tends to rotate the system about the shaft's axis.4. **Dimensions**: - From the point A (bearing) to the point C (left end of the plate) is 200 mm. - The length from point C to D across the plate is 600 mm, and the height of the plate is 400 mm.5. **Cable**: - A cable restrains the plate from rotating, fixed between points C and D.#### Given Data:- Uniform plate mass: 15 kg- Couple applied: 120 N·m- Distance between bearings A and B: 80 mm- Length of the plate from C to D: 600 mm- Height of the plate: 400 mm- Distance from top to bearing A: 200 mm- Distance from top to bearing B: 280 mm#### Required:Calculate the force supported by bearing B during the application of the 120 N·m couple.---This problem involves mechanics and strengths of materials principles to understand the forces acting on bearings and the resulting prevention of rotational motion due to an applied couple. Calculations will include moments and the equilibrium of forces for solution derivation.

Answered: Image /qna-images/answer/b94bedac-baf7-47c8-9612-79a415c1a7da.jpg

3/99 SS The uniform 15-kg plate is welded to the ver- ical shaft, which is supported by bearings A and B. Cal- ulate the magnitude of the force supported by bearing B luring application of the 120-N-m couple to the shaft. The cable from C to D prevents the plate and shaft from urning, and the weight of the assembly is carried en- irely by bearing A. 200 mm 120 N·m A B 200 mm PROBLEM 3/99 80 mm 600 mm 400 mm

3/99 SS The uniform 15-kg plate is welded to the ver- ical shaft, which is supported by bearings A and B. Cal- ulate the magnitude of the force supported by bearing B luring application of the 120-N-m couple to the shaft. The cable from C to D prevents the plate and shaft from urning, and the weight of the assembly is carried en- irely by bearing A. 200 mm 120 N·m A B 200 mm PROBLEM 3/99 80 mm 600 mm 400 mm

Steel Design (Activate Learning with these NEW titles from Engineering!)

6th Edition

ISBN:9781337094740

Author:Segui, William T.

Publisher:Segui, William T.

Chapter10: Plate Girders

Section: Chapter Questions

Problem 10.7.9P

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Question

### Problem 3/99

#### Problem Statement:
The uniform 15-kg plate is welded to the vertical shaft, which is supported by bearings A and B. Calculate the magnitude of the force supported by bearing B during application of the 120-N·m couple to the shaft. The cable from C to D prevents the plate and shaft from turning, and the weight of the assembly is carried entirely by bearing A.

#### Diagram Explanation:
The provided diagram illustrates the structural setup for the problem. Below is a detailed explanation of the diagram:

1. **Vertical Shaft and Plate**:
- A vertical shaft passes through and supports a horizontally oriented plate.
- The plate is denoted by points C and D, with C on the left and D on the right.

2. **Bearings**:
- There are two bearings labeled as points A and B.
- Bearing A is located at the upper part of the shaft, 200 mm down from the top.
- Bearing B is positioned 80 mm below bearing A, making it 280 mm down from the top of the shaft.

3. **Couple**:
- A twisting couple of 120 N·m is applied to the top of the shaft. This couple tends to rotate the system about the shaft's axis.

4. **Dimensions**:
- From the point A (bearing) to the point C (left end of the plate) is 200 mm.
- The length from point C to D across the plate is 600 mm, and the height of the plate is 400 mm.

5. **Cable**:
- A cable restrains the plate from rotating, fixed between points C and D.

#### Given Data:
- Uniform plate mass: 15 kg
- Couple applied: 120 N·m
- Distance between bearings A and B: 80 mm
- Length of the plate from C to D: 600 mm
- Height of the plate: 400 mm
- Distance from top to bearing A: 200 mm
- Distance from top to bearing B: 280 mm

#### Required:
Calculate the force supported by bearing B during the application of the 120 N·m couple.

---

This problem involves mechanics and strengths of materials principles to understand the forces acting on bearings and the resulting prevention of rotational motion due to an applied couple. Calculations will include moments and the equilibrium of forces for solution derivation.

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