Mechanics Of Materials
Mechanics Of Materials ME 32300
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This 17 page Class Notes was uploaded by Kristopher Beahan on Saturday September 19, 2015. The Class Notes belongs to ME 32300 at Purdue University taught by Staff in Fall. Since its upload, it has received 66 views. For similar materials see /class/207990/me-32300-purdue-university in Mechanical Engineering at Purdue University.
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Date Created: 09/19/15
SAMPLE PROBLEMS FOR MIDTERM 2 TYPICAL EQUATION SHEET Relevant Equations 1 8xE039x v039y039zaAT rGr 1 Tr gyEoy v039x039zaAT 1 gzi039Z v039x039yaAT E G 1 1 1 p lxy Erxy 7x2 57xz 7yz 67yz I 7rd4 039 1 vg vg 8 p 32 Z 1v1 2v Z Z Z I dgquotdf39 E l p 32 039 1 vg v 8Z8x y 1v1 2v y 0 from E 1 ltxagtn quotf gt quot0 1 2 3 039 v s v g g Z 1v1 2v Z Z Z x a 0 a I x a 1 for n S 0 FL ltx agtndx 1 e LOAT n1 gt0 EA n1ltx a forrz Failure Stress Yield Strength Allowable Stress State of Stress ExyMxy a 6 6 a oxayWT on Z2 y 2 yc0s26rvsin26 bh3 039 039 1 12 rectangle 1m 2 y sin26rxy 00526 g 2 b R ax 0yrz a 039x039y y 2 xy avg 2 QyLndAAy EIVquotM EIVquot39V EIVuu p PROBLEM 1 The simply supported beam shown below has a rectangular cross section The beam is required to support a concentrated load of 5000 lb and a distributed load of 5000 lbft 4 9 9939 gt1 Draw the free body diagram for the beam Determine the reaction forces at the supports Draw shear and moment diagrams for the entire beam note shear and moment equations will not receive any credits Determine the critical shear and moment locations along the beam Determine the normal bending and shear stresses for step 4 At X 10 ft from the left end of the beam determine the normal and shear stresses for the point B located at Z 05 in and Y l in as shown on the cross sectional area of the beam Determine the principal normal stresses and the absolute maximum shear stress for step 5000 lbft B AN 4m PROBLEM 2 A beam has a square cross section of 01 m by 01 m The beam is 4 m long with cantilever supports at both ends It is loaded with a linearly changing distributed load qx xq0L with qg40000 Nm Show a sketch of the exural stress distribution at the location 990 ie at support A of the beam PROBLEM 3 Given the plane stress state 0320 MPa 0550 MPa rxy10 MPa all other stress components zero at a point in a body a Draw Mohr circle and represent the stress state 0300 rxy on Mohr circle as points X and Y corresponding to the given stress state b Determine the principal stresses and the maximum inplane shear stress indicate them on Mohr s circle c Draw a correctly oriented stress element for the principal stress state as well as for the maximum inplan shear stress state indicate rotation relative to the xy coordinates and draw the stress vectors PROBLEM 4 A beam of lengthL consists of a material with elastic modulus E and possesses an area momentum of inertia I The beam is loaded by a moment Mg as shown in the gure Determine the equation for the de ection vx y M0 X A L 43 PROBLEM 5 Consider the beam shown below that is clamped firmly at A supported on a roller at B and loaded vertically downward by a point force at C Neglecting gravity for this beam 1 Draw the free body diagram for the beam and write down the equilibrium equations 2 Find the reaction force at the roller B 3 Draw the shear forcebending moment VM diagram for this beam 4 Write down the de ection curve in the region AB 5 Find the de ection at point C EI B EI C QF 3 PROBLEM 6 Three wood boards each of 15 X 35 in rectangular cross section are glued together to form a beam Assuming that the beam needs to withstand a vertical shear force V of 250 lbs b What is the required shear strength of the glue ie what shear stress should it be able to Withstand c Multiple choice The maximum shear stress occurs at the neutral axis The maximum shear stress occurs at the same location as the exural stress Neither of the above PROBLEM 7 Given the plane stress state 050 MPa 0510 MPa rxy40 MPa all other stress components zero at a point in a body d Draw Mohr s circle and represent the stress state 0300 rxy points X and Y e Determine the principal stresses and the maximum inplane shear stress and indicate them on Mohr s circle f Draw a properly oriented stress element for the principal stress state as well as for the maximum inplane shear stress state Indicate the rotations relative to the XaXis and draw the stress vectors PROBLEM 8 Find the reactions for the beam depicted below Assume that E is constant along the beam L2 LF L2 J I 39l PROBLEM 9 The beam below uniform E1 is supported by a pin joint and a roller and subject to loading all numbers in SI units as shown Sketch the shear force V and bending moment M diagrams for this loading All key values and slopes must be clearly listed on the diagrams 16 points Find an expression for the de ection curve and nd the de ection at points B and D 18 points N y Pluhlzm um Midterm 2 Sample Problem Answers b Ay 1625 kip Cy 3875 kip 0 1 Critical location at X 1225 ft max moment X 20 ft max shear e 33785 ksi I 727 ksi i GB1547 kSl EB 158 ksi g 51 15471 ksi 52 002 ksi Tmax 7736 ksi SA 1281 lPa a Hhi 134 b 51 5303 IVIPa 52 1697 1 Parmax 1803 MPa 0 9p2 1685 CW 9p1 7315 from horizontal 951 2816 CCW WWW TV P Lm 3 PH net 54 39 gtym ML uxi x3x2 Ox E1 6L 2 3 5 b By F e uu2L a 1211 psi b Max shear stress occurs at neutral axis b a 70 MPa 0 30 MPa rm 50 MP2 c 9 2555u ch es 1843 CW b WWW Wx WM w m 11 5 3 iFHB iFM 7 A 16 y 15 A 16 LVN I u IM A 5 RM L uh quotM L n u Lm WM i DL 39LHL 13wnL 16EI uL 7 L 48 H mom 10 Max shear stress occurs at 05 1110 Tmax 226 kPa