Question 1

A steel rod with a length of $$L = 2.0\ \mathrm{m}$$ and cross-sectional area $$A = 400\ \mathrm{mm}^2 is $$subjected to a tensile force of $$P = 50,000\ \mathrm{N}. If $$the modulus of elasticity for steel is $$E = 200\ \mathrm{GPa}$$, what is the axial deformation $$\Delta L of $$the rod? Use $$\Delta L = \dfrac{PL}{AE}.$$

Accepted Answer

$$1.25\ \mathrm{mm}$$

Question 2

A bridge is constructed using aluminum beams ($$E = 70\ \mathrm{GPa}$$, $$\alpha = 23 	imes 10$$^{-6}$$/^\circ\mathrm{C}). If a$$ $$5.0\ \mathrm{m}$$ beam experiences a temperature increase of $$30^\circ\mathrm{C}$$, what is the change in length $$\Delta L$$ due to thermal expansion? Use $$\Delta L = \alpha L \Delta T.$$

Accepted Answer

$$3.45\ \mathrm{mm}$$

Question 3

Which of the following statements about statically indeterminate members is correct?

Accepted Answer

Both equilibrium and compatibility of deformations must be used to solve for internal forces.

Question 4

A steel bar ($$E = 200\ \mathrm{GPa}$$, $$\alpha = 12 	imes 10$$^{-6}$$/^\circ\mathrm{C}) is $$fixed at both ends and subjected to a temperature increase of $$50^\circ\mathrm{C}. $$What is the thermal stress $$\sigma$$ developed in the bar? Use $$\sigma = E \alpha \Delta T.$$

Accepted Answer

$$120\ \mathrm{MPa}$$

Question 5

A rod is subjected to a compressive force. Which sign convention should be used for the resulting stress and deformation?

Accepted Answer

Stress and deformation are negative (compression).

Question 6

A steel pipe ($$E = 200\ \mathrm{GPa}) $$and an aluminum pipe ($$E = 70\ \mathrm{GPa}) $$are joined end-to-end and subjected to the same axial load. Which pipe will experience the greater deformation, assuming equal lengths and cross-sectional areas?

Accepted Answer

The aluminum pipe, because it has a lower modulus of elasticity.

Question 7

A bar with a hole in the middle is subjected to a tensile force. If the nominal stress is $$\sigma_{nom}$$ and the stress concentration factor is $$K_t = 2.5$$, what is the maximum local stress at the hole?

Accepted Answer

$$2.5\sigma_{nom}$$

Question 8

Why is it important to design smooth transitions (such as fillets) in structural members?

Accepted Answer

To reduce the stress concentration factor $$K_t$$ and prevent premature failure.

Question 9

A steel railway track ($$L = 10\ \mathrm{m}$$, $$\alpha = 12 	imes 10$$^{-6}$$/^\circ\mathrm{C}) is $$laid at $$10^\circ\mathrm{C}. If $$the temperature rises to $$40^\circ\mathrm{C}$$ and expansion is prevented, what is the compressive stress developed? ($$E = 200\ \mathrm{GPa})$$

Accepted Answer

$$72\ \mathrm{MPa}$$

Question 10

Which of the following best describes the relationship between load, deformation, and stiffness for an axially loaded member?

Accepted Answer

$$\Delta L = \dfrac{PL}{AE}$$, so greater stiffness ($$AE/L) $$means less deformation.

Question 11

A composite bar consists of a steel segment ($$E_s = 200\ \mathrm{GPa}$$, $$\alpha_s = 12 	imes 10$$^{-6}$$/^\circ\mathrm{C}) $$and an aluminum segment ($$E_a = 70\ \mathrm{GPa}$$, $$\alpha_a = 23 	imes 10$$^{-6}$$/^\circ\mathrm{C}$$), both $$1.0\ \mathrm{m}$$ long. If the temperature increases by $$40^\circ\mathrm{C}$$ and the bar is fixed at both ends, which segment will experience greater thermal stress?

Accepted Answer

The aluminum segment, because it wants to expand more but is less stiff.

Question 12

If a bar is loaded in tension and has a sudden change in cross-sectional area (such as a notch), what is the most likely effect?

Accepted Answer

A local increase in stress, possibly leading to failure at the notch.

Question 13

A $$2.0\ \mathrm{m}$$ long aluminum rod ($$A = 500\ \mathrm{mm}^2$$, $$E = 70\ \mathrm{GPa}) is $$subjected to a compressive force of $$P = 30,000\ \mathrm{N}. $$What is the axial deformation $$\Delta L$$?

Accepted Answer

$$1.71\ \mathrm{mm}$$

Question 14

Which of the following is a key reason why thermal expansion must be considered in the design of bridges and pipelines?

Accepted Answer

Restrained thermal expansion can generate significant internal stresses.

Question 15

A bar is subjected to an axial load $$P$$ and has a length $$L$$ and cross-sectional area $$A. If $$the modulus of elasticity $$E is $$doubled, what happens to the axial deformation $$\Delta L$$?

Accepted Answer

It is reduced by half.

Question 16

In a statically indeterminate system, which two principles must be applied to solve for unknown forces and deformations?

Accepted Answer

Equilibrium and compatibility of deformations.

Question 17

A steel bar ($$E = 200\ \mathrm{GPa}) $$with $$A = 300\ \mathrm{mm}^2$$ and $$L = 1.5\ \mathrm{m} is $$subjected to a compressive force of $$P = 70,000\ \mathrm{N}. $$What is the axial deformation $$\Delta L$$?

Accepted Answer

$$-1.75\ \mathrm{mm}$$

Question 18

Which of the following is NOT a correct practice for minimizing stress concentrations in engineering design?

Accepted Answer

Introducing sharp corners at transitions.

Question 19

A bar is loaded in tension with a force $$P$$ and has a cross-sectional area $$A. $$What is the formula for the normal stress $$\sigma in $$the bar?

Accepted Answer

$$\sigma = \dfrac{P}{A}$$

Axial Loads, Thermal Deformation, and Stress Concentrations

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