A flat plate specimen of a soft metal alloy is to be tested by pulling on round pins inserted through the ends of the plate, as illustrated below

(a) Calculate the required diameter of the pins, given that the plate is 8.0 mm thick, the maximum tensile load is 4.0 kN and the maximum allowable average bearing stress is 50 MPa.
(b) What stresses are apparent in the pins?

To calculate the required diameter of the pins, we need to consider the maximum allowable average bearing stress and the maximum tensile load.

(a) Calculation of the required diameter of the pins:

1. Start by calculating the maximum allowable bearing stress that the pins can withstand.
Maximum allowable bearing stress = 50 MPa

2. Determine the cross-sectional area of the pins based on the maximum tensile load that the plate can withstand.
Maximum tensile load = 4.0 kN = 4000 N
Cross-sectional area of the plate = thickness of the plate * width of the plate

3. Since the plate is assumed to be a flat plate, the width of the plate does not affect the load distribution on the pins, so we can ignore it for the calculation. Therefore, the cross-sectional area of the pins is equal to the cross-sectional area of the plate.

4. Cross-sectional area of the pins = thickness of the plate * width of the plate
Cross-sectional area of the pins = 8.0 mm * width of the plate

5. Now we need to solve for the width of the plate.
Cross-sectional area of the pins = Cross-sectional area of the plate
8.0 mm * width of the plate = Cross-sectional area of the plate

6. Rearrange the equation to solve for the width of the plate.
width of the plate = Cross-sectional area of the plate / 8.0 mm

7. Substitute the maximum tensile load and maximum allowable bearing stress into the equation to find the width of the plate.
width of the plate = (4000 N) / (50 MPa * 8.0 mm)

8. Convert the units of width from mm to meters.
width of the plate = (4000 N) / (50 MPa * 0.008 m)

9. Calculate the width of the plate.
width of the plate = 10 m

10. Finally, calculate the diameter of the pins.
Since the pins are assumed to be round, the width of the plate is also equal to the diameter of the pins.
diameter of the pins = width of the plate = 10 m

Therefore, the required diameter of the pins is 10 mm.

(b) To determine the stresses apparent in the pins, we need more information about the pins, such as the material they are made of, their dimensions, and the applied load. Without this information, it is not possible to calculate the stresses in the pins.