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What is the total angle of twist in radians for the following metal shaft? Answer to 4 decimal places [0.0000]. T = 1,544 lb-in, L = 1 ft, G = 9,290 ksi, J = 0.10 in^4 apguvor

What is the total angle of twist in radians for the following metal shaft? Answer to 4 decimal places [0.0000]. T = 1,544 lb-in, L = 1 ft, G = 9,290 ksi, J = 0.10 in^4 apguvor

Structural Analysis
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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**Problem Statement:** What is the total angle of twist in radians for the following metal shaft? Answer to 4 decimal places [0.0000]. **Given:** - Torque (T) = 1,544 lb-in - Length (L) = 1 ft - Shear Modulus (G) = 9,290 ksi - Polar Moment of Inertia (J) = 0.10 in^4 **Solution:** To solve this problem, we need to use the formula for the angle of twist (\(\theta\)) in a shaft: \[ \theta = \frac{{T \cdot L}}{{G \cdot J}} \] Convert all units to the same system before calculating. Specifically, ensure that the length (L) is in inches because the polar moment of inertia (J) is given in inches to the fourth power: Since \(1 \text{ ft} = 12 \text{ in}\), \[ \theta = \frac{{1,544 \text{ lb-in} \times 12 \text{ in}}}{{9,290,000 \text{ psi} \times 0.10 \text{ in}^4}} \] Calculate \(\theta\) and round the result to four decimal places.
Transcribed Image Text:**Problem Statement:** What is the total angle of twist in radians for the following metal shaft? Answer to 4 decimal places [0.0000]. **Given:** - Torque (T) = 1,544 lb-in - Length (L) = 1 ft - Shear Modulus (G) = 9,290 ksi - Polar Moment of Inertia (J) = 0.10 in^4 **Solution:** To solve this problem, we need to use the formula for the angle of twist (\(\theta\)) in a shaft: \[ \theta = \frac{{T \cdot L}}{{G \cdot J}} \] Convert all units to the same system before calculating. Specifically, ensure that the length (L) is in inches because the polar moment of inertia (J) is given in inches to the fourth power: Since \(1 \text{ ft} = 12 \text{ in}\), \[ \theta = \frac{{1,544 \text{ lb-in} \times 12 \text{ in}}}{{9,290,000 \text{ psi} \times 0.10 \text{ in}^4}} \] Calculate \(\theta\) and round the result to four decimal places.
Expert Solution
Step 1: Given data

Torque=T=1.544lb-in


length=L=1ft


ridigity=G=9290ksi


polar moment of inertia=J=0.1 space i n to the power of 4

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