# HES5320 Solid Mechanics, Semester 2, 2011, Group Assignment

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HES5320 Solid Mechanics, Semester 2, 2011, Group Assignment by Stephen, P. Y. Bong, Faculty of Engineering and Industrial Science, Swinburne University of Technology (Sarawak Campus)
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SWINBURNE UNIVERSITY OF TECHNOLOGY (SARAWAK CAMPUS)FACULTY OF ENGINEERING AND INDUSTRIAL SCIENCE HES5320 Solid Mechanics Semester 2, 2011 Group Assignment Lecturer: Dr. Saad A. MutasherByGroup No. 2Stephen Bong Pi Yiing (4209168)Ngui Yong Zit (4201205)Ling Wang Soon (4203364)Due Date: 5 pm, 28 th October 2011 (Friday)  Group AssignmentHES5320 Solid Mechanics, Semester 2, 2011 Group No. 2 Page 2 of  30   Question 1 For plate shown in Figure 1, use solidwork simulation to calculate the maximum principle stresses andtheir locations. The materials of plate is Alloy steel (  E  = 210 GPa, ν = 0.29). Use the option DesignScenario in solidwork to study the effect of hole diameter on principle stress. The diameters of hole are(20, 25, 30, 40, 50, 60, 70, 80, 90, 100) mm. Plot separately the graph of principle stress vs. hole diameter.Vertical axis of graphs should be stress and horizontal axis hole diameter. Discuss the results.Figure 1 Solutions Fig. Q1A and Fig. Q1B below shows the results of finite element analysis (FEA) simulation by usingSolidWorks and the plot of principle stress vs. hole diameter.Fig. Q1A: Locations of principle stresses obtained using SolidWorks FEA Simulation when the hole’sdiameter is 50 mm.  Group AssignmentHES5320 Solid Mechanics, Semester 2, 2011 Group No. 2 Page 3 of  30  Fig. Q1B: Plot of principle stress vs. hole diameter. Hole Diameter (mm) Principal Stresses (MPa) 20 4.991525 4.750730 4.951740 5.303550 5.816160 6.262170 6.392880 6.895290 7.1401100 7.2091Table 1: Variation of principle stresses with their respective hole diameter  Discussion : According to the definition of normal stress, dAdF  AF   A =∆∆= →∆ 0 lim σ   , which is a measurement of the amount of internal forces contained in a deformable materials. It can be also defined by the internalforce per unit area (P. P., Benham; R. J., Crawford & C. G., Armstrong, 1996, pp. 43). Mohr’s circle is analternative which represents all possible states of normal and shear stress on any plane through a stressedpoint. From the Mohr’s circle, the plane causes the material to experience zero shear stress is termedprincipal planes and the normal stresses acting on them are termed principal stresses which alwaysdenoted as ( σ 1 and σ 2 , or, σ max and σ min ) (P. P., Benham; R. J., Crawford & C. G., Armstrong, 1996, pp.298 & pp. 301). Based on the results obtained from the SolidWorks FEA simulation as shown in Fig.Q1A above, the magnitude of the principal stresses are 7.7 MPa and 0.4 MPa respectively. Apart fromthat, the stress is maximum at the necking of the plate and minimum at the top and bottom edges of thehole. When a load of 5 kN is applied at the free end of the plate, the plate experience uniform stressdistribution and the deformation only takes place in tangential direction of the applied load. When a hole 4.555.566.577.520 30 40 50 60 70 80 90 100    P  r   i  n  c   i  p  a   l   S   t  r  e  s  s ,      σ    (   M   P  a   ) Hole Diameter (mm) Principal Stress, σ  (MPa) vs. Hole Diameter (mm)  Group AssignmentHES5320 Solid Mechanics, Semester 2, 2011 Group No. 2 Page 4 of  30  is drilled with an offset of 0.25 m from the fixed end, the distribution of stresses deviates when the load of 5 kN is applied at the free end. The deviation of colours in the legend beside the simulation as shown inFig. Q1A above indicates the magnitude of principle stresses with respective to their locations. In order tostudy the effect of principle stresses resulted by various hole diameters, the top edge of the hole has beenselected as a reference point. According to the definition of normal stress,  AF  = σ   where F  is the appliedload and  A is the area normal to the applied force, the upsurge in hole diameters will results the reductionin area which consequence the increase in principle stress as shown in Fig. Q1B above.
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