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# 159 Note for ME 32300 at Purdue

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This 11 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15

SAMPLE PROBLEMS FOR MIDTERM 2 TYPICAL EQUATION SHEET Relevant Equations ex 039x v039y OZ aAT 8y 039y v039x azaAT gz 039Z v039x 039yaAT 1 1 73915739 7xz57xz 7yz57yz E 039 1 vgvg 8 tltHMFW xy 039 1 vg vgzgx y 1v1 2v y E O39Z ml1 vgz 18r 8 eEL0AT EA Failure Stress Yield Strength Allowable Stress State of Stress E Mm mm L 3 rectan 1e 12 g Q 3 gwLaMAr L39 EIVquotM EIv39quot V EIVuu p rGr L Tr T IF TL GIF 7239al4 p 32 Izmete p 32 n 0 lt ltx agt fax a n0123 x aquotf0rx2a x a 1 for n S 0 Iltx aquotdx 1 ltx a forngt0 n1 o x039y 0 0 0 y 00526r sin26 2 W 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 1 Draw the free body diagram for the beam 2 Determine the reaction forces at the supports 3 Draw shear and moment diagrams for the entire beam note shear and moment equations will not receive any credits 4 Determine the critical shear and moment locations along the beam 5 Determine the normal bending and shear stresses for step 4 6 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 7 Determine the principal normal stresses and the absolute maximum shear stress for step 6 Y 5000 lb Y A 5 ft 750001bft Bx A W 1 1 z r r r V v r X 4 m P v W1 1 D 10 ft 10 ft 2 1 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 3 A B X 4m 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 gtX A i 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 o 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 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 1 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 2 Find an expression for the de ection curve and nd the de ection at points B and D 18 points y El W0 I l LW l gtx B amp D L L L gt1 V p X Pluhlzm um

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