Practice Quiz

Explanation

Young's modulus is the slope of the stress-strain curve in the elastic region. It can be determined from Hooke's law:

$$\sigma = \varepsilon E$$

From the graph below we have $\sigma = 80 \mathrm{MPa}$ for a strain of 2%, which gives:

$$E = \frac{80 \mathrm{MPa}}{0.02} = 4 \mathrm{GPa}$$

Explanation

The 0.2% offset method is used to determine the yield strength of a material from the stress-strain curve, and is particularly useful for cases where the is no sudden transition from elastic to plastic behavior.

It involves drawing a line that has a slope equal to Young's modulus, and offsetting it along the horizontal axis by a strain of 0.2%.

For this stress-strain curve, using the 0.2% offset method gives a yield strength of 300 MPa.

Explanation

Resilience is the ability of a material to deform elastically without permanent plastic deformation. Highly resilient materials are able to absorb large amounts of energy without deforming plastically.

The modulus of resilience is the strain energy per unit volume that can be absorbed without plastic deformation, from zero strain up to the elastic limit. It is equal to the area under the stress-strain curve, up to the yield point.

Explanation

A zero force member is a member of a truss that carries no load.

If three members are connected at a single joint, and two of the members are collinear, the third member is always a zero force member, so long as no external forces act on the joint. This configuration is shown in the image below.

This is because only the third member applies a force to the joint in the vertical direction, so to maintain equilibrium of forces in the vertical direction at the joint the force in that member must be zero.

This is the case at joint C, so member B-C must be a zero force member.

Explanation

The theoretical mechanical advantage of a gear system can be calculated using the ratio of the number of teeth on the driven gear (Gear B) to the number of teeth on the driving gear (Gear A):
$$MA = \frac{24}{8} = 3$$
The mechanical advantage of 3 means that the gear system multiplies the input torque by 3, assuming no losses due to friction or other factors. The torque value of 20 Nm is not used in determining the answer to this question.