Q: A steel rod is subjected to a tensile force. If its original length is $$L$$ and the change in length is $$\Delta L$$, what is the axial strain?

$$\text{Axial Strain} = \frac{\Delta L}{L}$$

Q: Given the coefficient of linear expansion for steel is $$11.7 \times 10$$^{-6}$$ mm/mm/$$^\circ$$C, what is the change in length $$\Delta L$$ for a steel rod of length L = 1000$ mm subjected to a temperature increase $$\Delta T = 30^\circ$$C?

$$\Delta L = (11.7 \times 10$$^{-6}$$) \times 1000 \times 30 = 0.351 mm$$

Q: If the stress in concrete $$f_C is 11.5 $$MPa and the modular ratio $$n is 7.41$$, what is the stress in steel $$f_S$$?

$$f_S = n f_C = 7.41 \times 11.5 = 85.2$$ MPa

Q: A steel bar is loaded in tension. If the original width is $$w$$ and the change in width is $$\Delta w$$, what is the transverse strain?

$$\text{Transverse Strain} = \frac{\Delta w}{w}$$

Question 1

Which of the following best describes Poisson’s Ratio for a material?

Accepted Answer

It is the ratio of the transverse strain to the axial strain.

Question 2

A steel rod is subjected to a tensile force. If its original length is $$L$$ and the change in length is $$\Delta L$$, what is the axial strain?

Accepted Answer

$$	ext{Axial Strain} = \frac{\Delta L}{L}$$

Question 3

If a concrete column is reinforced with steel, why is steel used in combination with concrete?

Accepted Answer

Steel is strong in tension while concrete is strong in compression.

Question 4

A member experiences a drop in temperature. What happens to its dimensions?

Accepted Answer

All dimensions decrease.

Question 5

Given the coefficient of linear expansion for steel is $$11.7 	imes 10$$^{-6}$$ mm/mm/$$^\circ$$C, what is the change in length $$\Delta L$$ for a steel rod of length L = 1000$ mm subjected to a temperature increase $$\Delta T = 30^\circ$$C?

Accepted Answer

$$\Delta L = (11.7 	imes 10$$^{-6}$$) 	imes 1000 	imes 30 = 0.351 mm$$

Question 6

For a composite column made of concrete and steel, if the modulus of elasticity for steel is $$E_S = 200,000$$ MPa and for concrete $$E_C = 27,000$$ MPa, what is the modular ratio $$n$$?

Accepted Answer

$$n = \frac{E_S}{E_C} = \frac{200,000}{27,000} = 7.41$$

Question 7

A composite column is subjected to a total axial load $$P_{TOTAL}. If $$the area of concrete is $$A_C$$ and the area of steel is $$A_S$$, and the modular ratio is $$n$$, what is the formula for the stress in concrete $$f_C$$?

Accepted Answer

$$f_C = \frac{P_{TOTAL}}{A_C + n A_S}$$

Question 8

If the stress in concrete $$f_C is 11.5 $$MPa and the modular ratio $$n is 7.41$$, what is the stress in steel $$f_S$$?

Accepted Answer

$$f_S = n f_C = 7.41 	imes 11.5 = 85.2$$ MPa

Question 9

A steel bar is loaded in tension. If the original width is $$w$$ and the change in width is $$\Delta w$$, what is the transverse strain?

Accepted Answer

$$	ext{Transverse Strain} = \frac{\Delta w}{w}$$

Question 10

If a member is loaded in compression and its original length is $$L$$, which of the following occurs?

Accepted Answer

The member gets shorter and fatter.

Question 11

A concrete cylinder with diameter $$d = 136 mm $$and height $$h = 329 mm is $$axially compressed by a load $$P = 1409 kN. If $$the height decreases by $$1.43 mm $$and the circumference increases by $$0.800 mm$$, what is the modulus of elasticity $$E$$ for the concrete?

Accepted Answer

$$E = 22.3$$ GPa

Question 12

Which of the following statements about Poisson’s Ratio is correct?

Accepted Answer

Poisson’s Ratio is unitless and is a constant for each material.

Question 13

A steel bar has an original length $$L = 2774 mm. $$After loading, its length increases by $$54 mm. $$What is the new length?

Accepted Answer

$$2774 + 54 = 2828 mm$$

Question 14

If a member is subjected to a temperature change but is not allowed to expand or contract, what type of stress develops?

Accepted Answer

Thermal stress

Question 15

For a composite column, if the total load $$P_{TOTAL} is 800 kN$$, the force carried by concrete $$P_C is 460 kN$$, and each steel plate carries $$P_{S1} = P_{S2} = 170 kN$$, which equation is correct?

Accepted Answer

$$P_{TOTAL} = P_C + P_{S1} + P_{S2}$$

Question 16

A composite column is made of concrete and steel, bonded together. What is true about the strain in each material under load?

Accepted Answer

Both materials experience the same strain.

Question 17

If the sides of a member are not restrained, what is the transverse stress?

Accepted Answer

Transverse stress is zero.

Question 18

Which equation is used to calculate the change in length due to temperature for a material?

Accepted Answer

$$\Delta L = \alpha L \Delta T$$

Question 19

A steel rod has a Poisson’s Ratio of 0.25. If the axial strain is $$0.002$$, what is the transverse strain?

Accepted Answer

$$0.25 	imes 0.002 = 0.0005$$

Stress Considerations in Statics & Strength of Materials

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