Task 1
Apply the relationship between longitudinal and transverse strain to determine the dimensional effects of uniaxial loading on a given system
1. A rectangular steel plate 180mm long and 45mm wide is subject to a tensile load along its length. If the width of the plate contracts by 0.005mm, find the change in length. The Poisson's ratio for the steel is 0.28.
Task 2
Determine the effects of two-dimensional and three dimensional loading on the dimensions of a given material
2. The rectangular steel plate shown in figure 1 below is subject to stresses in the x and y directions. Strains in these directions are measured as 5.54 ×10-5 in the x direction and 6.24 ×10-6 in the y direction. Find the stresses in the x and y directions if the material has a modulus of elasticity of 200GPa and a Poisson's ratio of 0.28?
3. Determine the stresses and strains in the three dimensions of the steel plate shown in figure 2 below under the loading shown. The material has a modulus of elasticity of 200GPa and Poisson's ratio of 0.27.
Task 3
Determine volumetric strain and change in volume due to three-dimensional loading
4. For the steel plate in Task 2 Q3 above, determine the change in volume which results from the loading shown.
5. A bar of circular cross section is subject to a tensile load of 100kN which is in the elastic range. The bar is made from a steel with E= 200 GPa and Poisson's ratio = 0.28. It has a diameter of 24mm and is 1.4 m long. Find the extension of the bar, the decrease in diameter and the increase in volume of the bar.
Task 4
Apply the relationship between elastic constants
6. An aluminium alloy has a modulus of elasticity of 80 GPa and a modulus of rigidity of 30GPa. Find the value of Poisson's ratio and the bulk modulus.
Task 5
Apply the relationship between bending moment, slope and deflection to determine the variation of slope and deflection along a simply supported beam
Analyse engineering situations and solve engineering problems using calculus
7. A simply supported beam has length 3.4m, and carries a uniform loading of 18kN/m and a concentrated load of 60kN. If the beam has a flexural stiffness of 45 MNm2:
a. Calculate the maximum values of slope and deflection
b. State where on the beam they are located.
Task 6
Determine the principal stresses that occur in a thin walled pressure vessel
8. A thin cylindrical pressure vessel has an internal diameter of 60mm and is made of steel of thickness 2.5mm. If it is subject to internal pressure of 18MPa and assuming the walls are seamless, find:
a. The circumferential stress at the wall
b. The longitudinal stress at the wall
c. The radial stress at the wall
Task 7
Determine the distribution of stresses in a pressurised thick walled cylinder
9. A thick cylinder has an internal diameter 200mm and external diameter 290mm. The cylinder is subject to an internal pressure of 80MPa and an external pressure of 44MPa. Find:
a. The hoop and radial stress at the inner and outer surfaces of the cylinder and
b. The longitudinal stress. The cylinder is assumed to have closed ends.