# Question: learning goal to calculate the elastic deflection in an axially...

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**Learning Goal:**

To calculate the elastic deflection in an axially loaded member.

For a bar subject to axial loading, the change in length, or deflection, between two points A and Bis δ=∫L0N(x)dxA(x)E(x), where N is the internal normal force, A is the cross-sectional area, E is the modulus of elasticity of the material, L is the original length of the bar, and x is the position along the bar. This equation applies as long as the response is linear elastic and the cross section does not change too suddenly.

In the simpler case of a constant cross section, homogenous material, and constant axial load, the integral can be evaluated to give δ=NLAE. This shows that the deflection is linear with respect to the internal normal force and the length of the bar.

In some situations, the bar can be divided into multiple segments where each one has uniform internal loading and properties. Then the total deflection can be written as a sum of the deflections for each part, δ=∑NLAE.

The circular rod shown (Figure 1) has dimensions d1 = 7.6 cm , L1 = 6 m , d2 = 3 cm , and L2 = 5 m with applied loads F1 = 140 kN and F2 = 55 kN . The modulus of elasticity is E = 100 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C.

Part A - Reaction force

What is the reaction force at A? Let a positive reaction force be to the right.

Express your answer with appropriate units to three significant figures.

Part B - Segment the rod

For the given rod, which segments must, at a minimum, be considered in order to use δ=∑NLAE to calculate the deflection at D?

Check all that apply.

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Check all that apply.

BD |

CD |

AD |

BC |

AC |

AB |

Part C - Calculate the deflection

What is the deflection of the end of the rod, D? Let a positive deflection be to the right.

Express your answer with appropriate units to three significant figures.

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