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ENGIN2301 MECHANICS OF SOLIDS
ASSESSED TUTORIAL 1
Question 1
Figure 1. Platform ABD supported by cable DE and strut BC.
Figure 1 shows a platform ABD that is supported by a cable DE and a strut BC. The platform is pinned at A and has a roller support at B. The pin connection is assumed in single-shear configuration as shown in the inset. The dimensions relevant to the inset are ???????? = 0.15 ????;
???? = 0.05 ???? and ???????? = 0.2 ????.
The platform supports a distributed load ???? = 200 ????????/????. If the tension in the cable ???????????? = 50 ????????, determine the following:
1. The reaction forces at the pin support at A and the roller support at B
2. The stress in the strut BC. Assume that the cross sectional area of the strut BC is ???????????? = 0.2 ????2.
3. The shear stress in the bolt in the pin connection at A
4. The bearing stresses in the flange plate and the platform at the pin connection at A
Question 2
Figure 2 shows a part of a component that is designed to support part of a machine. An initial static analysis has been carried out and the reaction forces acting on the component are as shown. The resultant external load acting on the component can be assumed to be located at point G. The component is supported by two bolts at A and B. Both bolts are under single shear configurations. For the configuration shown in the figure, determine the following:
1. The reaction forces ????????, ???????? and ????
2. The shear stresses experienced by the bolts at A and B
Figure 2. Part of a component supporting force at G.
Question 3
Figure 3. Platform AD supported by non-uniform prismatic bars ABC and DEF.
Figure 3 shows a platform that supports a weight ???????? = 2000 ???? at its centre. A concentrated load ???? = 3000 ???? acts 360 ???????? away from the weight of the platform. The platform is supported at A and D by non-uniform bars ABC and DEF.
The non-uniform bars ABC and DEF are identical. The sections AB and DE are made of steel with Young’s modulus ???????????????????????? = 210 ???????????? and the section BC and EF are made of aluminium with Young’s modulus ???????????????????????????????????? = 80 ????????a. The lengths of the sections in the non-uniform bars are LAB = LDE = 200 mm and LBC = LEF = 50 mm. Both non-uniform bars have solid circular cross sections with diameter dAB = dDE = 15 mm and dBC = dEF = 40 mm.
Determine the total deformation of the non-uniform bars ABC and DEF.
Note: Assume that the non-uniform bars can only support load along their axis.
Question 4
Figure 4. An assembly of non-uniform shafts subjected to torques.
Figure 4 shows an assembly of non-uniform torsion subjected to torques at B, C and D. The
shear modulus of each section of the shafts are ???????????? = 80 ????????????, ???????????? = 120 ???????????? and ???????????? = 60 ????????????. The diameters of the shafts are as shown in the figure.
Determine the following:
1. The maximum stresses in each section AB, BC and CD based on the abovementioned angle of twist.
2. The total angle of twist (in degrees) of the non-uniform shafts when subjected to the load shown.