**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.

Answered: What is the total angle of twist in…

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

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

Connections

In steel structures, connections are the members that join two or more steel members. The connections are the most important members of any steel structure, and hence, they are designed more carefully. The majority of the construction cost of steel structures is incurred due to the connections. The design of connections is done as per the recommendations and specifications of the American Institute of Steel Construction (AISC).

Question

**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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