## Calculating stress and strain on Loading Systems.

Calculating stress and strain on Loading Systems.

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 : Young’s 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 4µm.

Calculate :

(a) The yield stress of the material (b) The force required to produce yield.

Young’s 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 Young’s 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 Young’s 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 µε indicate?