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Problem 5 A bar AC of length 20 mm increases linearly in diameter from 1 mm at point A to 3 mm at point C. Point A is anchored to a solid support. At point B, half-way between points A and C, forces of 100 N are applied to the top and the bottom of the beam, as shown. The ultimate shear stress in the beam is 250 GPa, while the ultimate tensile and 1 mm 100 N TC B A C 3 mm 100 N✓ 20 mm compressive stresses are both 500 GPa. To simplify your calculations, you can assume that this bar will fail due to ultimate shear stress, not tensile or compressive stress. (Can you explain why? Try, but then check the key later this week to make sure you understand.). What is the maximum torque Tc you can apply (in the direction shown) to point C before the bar is expected to fail? Hints: 1) Is this a deformation problem, where you need to find the stresses at all values of x, or a failure problem, where you just need to find the position(s) of maximum stress? 2) This has more than one segment, so for each segment, you will need a different equation to calculate deformations or a different position of maximum stress. 3)

Problem 5 A bar AC of length 20 mm increases linearly in diameter from 1 mm at point A to 3 mm at point C. Point A is anchored to a solid support. At point B, half-way between points A and C, forces of 100 N are applied to the top and the bottom of the beam, as shown. The ultimate shear stress in the beam is 250 GPa, while the ultimate tensile and 1 mm 100 N TC B A C 3 mm 100 N✓ 20 mm compressive stresses are both 500 GPa. To simplify your calculations, you can assume that this bar will fail due to ultimate shear stress, not tensile or compressive stress. (Can you explain why? Try, but then check the key later this week to make sure you understand.). What is the maximum torque Tc you can apply (in the direction shown) to point C before the bar is expected to fail? Hints: 1) Is this a deformation problem, where you need to find the stresses at all values of x, or a failure problem, where you just need to find the position(s) of maximum stress? 2) This has more than one segment, so for each segment, you will need a different equation to calculate deformations or a different position of maximum stress. 3)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.4: Applications
Problem 9EQ
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Problem 5 A bar AC of length 20 mm increases linearly in diameter from 1 mm at point A to 3 mm at point C. Point A is anchored to a solid support. At point B, half-way between points A and C, forces of 100 N are applied to the top and the bottom of the beam, as shown. The ultimate shear stress in the beam is 250 GPa, while the ultimate tensile and 1 mm 100 N TC B A C 3 mm 100 N✓ 20 mm compressive stresses are both 500 GPa. To simplify your calculations, you can assume that this bar will fail due to ultimate shear stress, not tensile or compressive stress. (Can you explain why? Try, but then check the key later this week to make sure you understand.). What is the maximum torque Tc you can apply (in the direction shown) to point C before the bar is expected to fail? Hints: 1) Is this a deformation problem, where you need to find the stresses at all values of x, or a failure problem, where you just need to find the position(s) of maximum stress? 2) This has more than one segment, so for each segment, you will need a different equation to calculate deformations or a different position of maximum stress. 3)
Transcribed Image Text:Problem 5 A bar AC of length 20 mm increases linearly in diameter from 1 mm at point A to 3 mm at point C. Point A is anchored to a solid support. At point B, half-way between points A and C, forces of 100 N are applied to the top and the bottom of the beam, as shown. The ultimate shear stress in the beam is 250 GPa, while the ultimate tensile and 1 mm 100 N TC B A C 3 mm 100 N✓ 20 mm compressive stresses are both 500 GPa. To simplify your calculations, you can assume that this bar will fail due to ultimate shear stress, not tensile or compressive stress. (Can you explain why? Try, but then check the key later this week to make sure you understand.). What is the maximum torque Tc you can apply (in the direction shown) to point C before the bar is expected to fail? Hints: 1) Is this a deformation problem, where you need to find the stresses at all values of x, or a failure problem, where you just need to find the position(s) of maximum stress? 2) This has more than one segment, so for each segment, you will need a different equation to calculate deformations or a different position of maximum stress. 3)
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