High school

Math Problem

Engineering and Construction

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UCL TEST Name: Institution: Engineering and Construction Test for applicants in UCL, Structures, Fluid Mechanics, Materials, and Soil Mechanics QUESTION 1 First determine whether the structure is statically determinate or indeterminate using 2n= m + r, where n= joints, m= members, r=reactions In this case, n=11, m=19, r=3 thus 2x11=22=19+3 therefore the structure is statically determinate Let the length of each of the 5 bays be x, Determine the reactions at the supports = (1+1+1+1+1)/2 = 2.5 units, simply because the truss is symmetrical about the apex.

AC= -2.5/sinO Sum of forces in the x-axis=o AB+CcosO=0, AB=-2.5/sinOXcosO=2.5/tanO Joint C 1 D C A B Sum of forces in the y-axis=0 -CA sinO+ CD sinO-1- CB cosO=0 Sum of forces in the x-axis=o -CA cosO+C D cosO+ CBsinO=0 Solving the equations we find CD &CB Joint B D C A B E Sum of forces in the y-axis=0 BC cosO+ BD cosO =0 Sum of forces in the x-axis=o -BA + BC sinO + BE +BD sinO =0 Solving we get BD and BE Joint D 1 F D C E B Sum of forces in the y-axis=0 -DC cosO+D F cosO- DBcos(90-O)-DE cos O -1=0 Sum of forces in the x-axis=o -DC sinO+ DF sinO- DBsin(90-O)-DE sin O =0 Solving we get DF QUESTION 2 Introduction Prestressing is normally accomplished in 3 ways which are: pre-tensioned concrete, followed by bonded and the unbonded and post-tensioned concrete. Pre-tensioned concrete is then cast all around the already tensioned tendons. Using this method results in a good bond in between the tendon and the concrete that both safeguards the tendon from sources of corrosion as well as allowing for direct transmission of tension. ...

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