# MECHANICAL PRINCIPLES DISTINCTION In addition to the Merit Criteria the student must : 1 Select and use appropriate equations for the calculation of stresses and strains. Calculate the change in dimensions resulting from the applied stresses and strains. Determine deflection due to shear strain. All calculations to use appropriate methods, values and units. 2 Calculate the yield stress, given the yield strain. Determine the applied force. All calculations to use appropriate methods, values and units. Solutions are rationally set out, clearly showing formulas used, transposition, values, answers and units. 3 Select the appropriate equation to calculate the bulk modulus of the material Determine the correct value for the bulk modulus, and express in appropriate units. Solutions are rationally set out, clearly showing formulas used, transposition, values, answers and units. 4 Select the appropriate equation to calculate the poisons ratio value given G and E Determine the correct value for poisons ratio. Solutions are rationally set out, clearly showing formulas used, transposition, values, answers and units. 5 Use appropriate methods Correct values for shear Correct values for for determining shear force, bending moment and deflection. force and bending moment. deflections, graph plotted with appropriate axes, values and units. 6 Select and use appropriate equation to calculate the maximum allowable pressure. Select appropriate equations for the calculation of the pressure, given hop strain value. Solutions are rationally set out, clearly showing formulas used, transposition, values, answers and units. 1. FIG 1 (All dimensions in mm) The component shown in Fig 1 is made from a material with the following properties and is subjected to a compressive force of 5kN. Material Properties : Youngs Modulus of Elasticity 200 GNm-2 Modulus of Rigidity 90 GNm-2 Poisons ratio 0.32 Calculate : (a) The stress in : (i) the circular section (ii) the square section (b) The strain in : (i) The circular section (ii) The square section (c) The change in length of the component (d) The change in diameter of the circular section (e) The change in the 40mm dimension on the square section (f) If the same component were subjected to a shear force of 7 kN as shown in FIG 2, calculate the shear strain in : (i) The circular section (ii) The square section FIG 2 2. When the 5mm diameter bar shown in FIG 3 is subjected to a tensile force F, yield occurs when the bar has extended by 4m. Calculate : (a) The yield stress of the material (b) The force required to produce yield. Youngs Modulus for the bar material is 150 GNm-2 Fig 3 3. A material is formed into a solid sphere and has a diameter of 100mm when at a pressure of 2MPa. If the diameter of the sphere reduces by 0.1mm when the pressure is increased to 6MPa, determine the bulk modulus of the material. 4. A material has a modulus of rigidity of 100 GNm-2 and a Youngs Modulus of 250 GNm-2. Calculate the expected value of poisons ratio for the material. 5. The simply supported beam shown in FIG 4 is 5m long with a Youngs Modulus of 210 GNm-2. The cross section of the beam is as shown in FIG 5. FIG 4 FIG 5 (a) Draw the shear force diagram for the beam (b) Determine the position and magnitude of the maximum bending moment. (c) Plot a graph of deflection along the length of the beam (calculate the deflection at 1m intervals). 6. A cylindrical vessel 2m internal diameter and 4m long has a wall thickness of 6mm. Strain gauges are installed on the vessel to measure hoop strain (see FIG 6). FIG 6 E = 290 GNm-2 Yield Stress = 500 MPa (i) What is the maximum allowable pressure if a factor of safety of 4 is to be used? (ii) What pressure would a strain of 40 e indicate?

MECHANICAL PRINCIPLESDISTINCTION

In addition to the Merit Criteria the student must :

1

Select and use appropriate equations for the calculation of stresses and strains.

Calculate the change in dimensions resulting from the applied stresses and strains.

Determine deflection due to shear strain. All calculations to use appropriate methods, values and units.

2

Calculate the yield stress, given the yield strain.

Determine the applied force.

All calculations to use appropriate methods, values and units.

Solutions are rationally set out, clearly showing formulas used, transposition, values, answers and units.

3

Select the appropriate equation to calculate the bulk modulus of the material

Determine the correct value for the bulk modulus, and express in appropriate units.

Solutions are rationally set out, clearly showing formulas used, transposition, values, answers and units.

4

Select the appropriate equation to calculate the poisons ratio value given G and E

Determine the correct value for poisons ratio.

Solutions are rationally set out, clearly showing formulas used, transposition, values, answers and units.

5

Use appropriate methods

Correct values for shear

Correct values for

for determining shear force, bending moment and deflection.

force and bending moment.

deflections, graph plotted with appropriate axes, values and units.

6

Select and use appropriate equation to calculate the maximum allowable pressure.

Select appropriate equations for the calculation of the pressure, given hop strain value.

Solutions are rationally set out, clearly showing formulas used, transposition, values, answers and units.

1.

FIG 1 (All dimensions in mm)

The component shown in Fig 1 is made from a material with the following properties and is subjected to a compressive force of 5kN.

Material Properties :

Youngs Modulus of Elasticity 200 GNm-2

Modulus of Rigidity 90 GNm-2

Poisons ratio 0.32

Calculate :

(a) The stress in :

(i) the circular section

(ii) the square section

(b) The strain in :

(i) The circular section

(ii) The square section

(c) The change in length of the component

(d) The change in diameter of the circular section

(e) The change in the 40mm dimension on the square section

(f) If the same component were subjected to a shear force of 7 kN as shown in

FIG 2, calculate the shear strain in :

(i) The circular section

(ii) The square section

FIG 2

2. When the 5mm diameter bar shown in FIG 3 is subjected to a tensile force F,

yield occurs when the bar has extended by 4m.

Calculate :

(a) The yield stress of the material

(b) The force required to produce yield.

Youngs Modulus for the bar material is 150 GNm-2

Fig 3

3. A material is formed into a solid sphere and has a diameter of 100mm when at a

pressure of 2MPa. If the diameter of the sphere reduces by 0.1mm when the

pressure is increased to 6MPa, determine the bulk modulus of the material.

4. A material has a modulus of rigidity of 100 GNm-2 and a Youngs Modulus of 250

GNm-2. Calculate the expected value of poisons ratio for the material.

5. The simply supported beam shown in FIG 4 is 5m long with a Youngs Modulus

of 210 GNm-2. The cross section of the beam is as shown in FIG 5.

FIG 4

FIG 5

(a) Draw the shear force diagram for the beam

(b) Determine the position and magnitude of the maximum bending moment.

(c) Plot a graph of deflection along the length of the beam (calculate the deflection

at 1m intervals).

6. A cylindrical vessel 2m internal diameter and 4m long has a wall thickness of 6mm. Strain gauges are installed on the vessel to measure hoop strain (see FIG 6).

FIG 6

E = 290 GNm-2

Yield Stress = 500 MPa

(i) What is the maximum allowable pressure if a factor of safety of 4 is to be used?

(ii) What pressure would a strain of 40 e indicate?