Highlights
The students will show an understanding of the principles of mechanics for bending and the following sub-learning outcome should be achieved, which the students will:LO4: obtain and analyze results of stress analysis for a representative engineering application.
The specification of tasks
A. cantilever beam has a cross-section of rectangle and has a height of 10mm and length of 100mm. The beam is made of mild steel with Young’s modulus of 210000 N/mm2 and Poisson’s ratio of 0.3.
1) Using 4 node quadrilateral elements (182),
i) With element numbers of 10, 40, 80 & 120 respectively to determine the tip deflection and maximum stress and position when a force of 100N is applied at the tip when the thickness is 2mm. Determine the smaller element number at which the tip deflection is converged.
ii) With a satisfactory element number from section 1,) i), to determine the thickness of the beam when yielding stress of the material is 370N/mm2
2) With beam elements (2 nodes 188), to determine the tip deflection and maximum stress and position when a force of 200N is applied at the tip when the required thickness is obtained with 4 node quadrilateral element in task 1(ii). Please note that the maximum number of beam elements must be less than 50.
3) Calculate the maximum deflection at the loading position with the following equations
where P is the force loaded at the tip, l is the length of the cantilever beam and E is Young’s
modulus of the beam material.
4) Compare the values of deflections at the loading tip with three methods.
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