### Problem StatementRod AB is made of steel (E = 29 x \(10^6\) psi), and rod BC is made of aluminum (E = 10.4 x \(10^6\) psi). If force \(Q = 10\) kips, \(R = 5\) kips, and \(P = 5\) kips, find the deflections of points B and D.### Diagram Explanation- **Structure Overview**: The diagram illustrates a composite rod consisting of two sections, AB and BC. - **Section AB**: - **Material**: Steel - **Modulus of Elasticity (E)**: 29 x \(10^6\) psi - **Diameter**: 3 inches - **Length**: 24 inches- **Section BC**: - **Material**: Aluminum - **Modulus of Elasticity (E)**: 10.4 x \(10^6\) psi - **Diameter**: 1 inch - **Total Length**: 20 inches (comprising two 10-inch segments) - **Forces**: - **Q**: 10 kips, applied at the start of the steel section. - **R**: 5 kips, applied between points C and D on the aluminum section. - **P**: 5 kips, applied at the end of the aluminum section at D.### TaskCalculate the deflections at points B and D due to the applied forces on this composite rod structure.

Answered: Image /qna-images/answer/f8c6e7e1-d607-4ce3-a5ed-60373a821e1b.jpgRod AB:Modulus of Elasticity (ES) = 29×106 psiArea (AAB) = π4DAB2 = π4×32 = 7.07 in.2Rod BD :Modulus of Elasticity (EA) = 10.4×106 psiArea (ABD) = π4×DBD2 = π4×12 = 0.7854 in.2∑FX = 00 = - RA - 10 + 5 + 5RA = 0 kipDeflection at B∂AB = PLAEAB = 0 in.Deflection at D (∂D) = ∂AB + ∂BD= 0 + PLAEBD= 10×103×20 0.7854×10.4×106∂D= 0.0245 in.∂B = 0 in.∂D = 0.0245 in.

Answered: Rod AB is made of steel (E = 29x10…

Engineering

Civil Engineering

Rod AB is made of steel (E = 29x10 psi), and rod BC is made of aluminum (E = 10.4x10° psi). If force Q = 10 kips, R =5 kips and P = 5 kips, find the deflections of points B and D.

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

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

### Problem Statement

Rod AB is made of steel (E = 29 x \(10^6\) psi), and rod BC is made of aluminum (E = 10.4 x \(10^6\) psi). If force \(Q = 10\) kips, \(R = 5\) kips, and \(P = 5\) kips, find the deflections of points B and D.

### Diagram Explanation

- **Structure Overview**: The diagram illustrates a composite rod consisting of two sections, AB and BC.
- **Section AB**:
- **Material**: Steel
- **Modulus of Elasticity (E)**: 29 x \(10^6\) psi
- **Diameter**: 3 inches
- **Length**: 24 inches

- **Section BC**:
- **Material**: Aluminum
- **Modulus of Elasticity (E)**: 10.4 x \(10^6\) psi
- **Diameter**: 1 inch
- **Total Length**: 20 inches (comprising two 10-inch segments)

- **Forces**:
- **Q**: 10 kips, applied at the start of the steel section.
- **R**: 5 kips, applied between points C and D on the aluminum section.
- **P**: 5 kips, applied at the end of the aluminum section at D.

### Task

Calculate the deflections at points B and D due to the applied forces on this composite rod structure.

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ISBN:

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