Practice Quiz

Explanation

Mohr's circle is a graphical representation of the state of stress at a point.

The maximum shear stress is represented by the diameter of the circle. The maximum and minimum principal stresses are the stresses for which the shear stress is equal to zero. And the average normal stress is equal to the centre of the circle.

Explanation

Because Gear B has more teeth than Gear A, one full rotation of Gear A will correspond to less than one full rotation of Gear B. This means Gear B must be rotating at a lower speed than Gear A.

The speed of gears in a gear train is inversely proportional to the number of teeth they have, based on the gear ratio. The gear ratio can be determined using the formula:
$$\mathrm{Gear Ratio} = \frac{\mathrm{Teeth_{Gear A}}}{\mathrm{Teeth_{Gear B}}} = \frac{12}{36} = \frac{1}{3}$$
If Gear A rotates at 1800 RPM, Gear B will rotate at:
$$\frac{1800\mathrm{RPM}}{3} = 600 \mathrm{RPM}$$

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

Because of the symmetry of the applied loading the vertical reaction force at each of the two the supports must be 5 kN. At the mid-point of the beam the 5 kN reaction force and the 5 kN applied force will cancel each other out, resulting in a shear force of zero over the middle section of the beam.

The shear force diagram is shown below.

Explanation

The size of the stiffness matrix is determined by the number of degrees of freedom (DOFs) associated with the element. Each node has a certain number of DOFs depending on the type of analysis. Thus, as the number of nodes in an element increases, the number of DOFs and hence the size of the stiffness matrix increase.