Name Score out of 100 E MCH 213 Strength of Materials Sample Final Exam 1 INSTRUCTIONS 1 Read the problems carefully 2 Show ALL work in a neat and logical order Partial credit will only be given if the work and reasoning are shown clearly and legibly Begin each problem by clearly indicating what you are trying to FIND 3 Your exam should contain 4 problems on separate pages and 1 page of short answer and multiple choice concept questions If something is missing notify a proctor immediately 4 Every internal load used must be clearly shown on a Free Body Diagram 5 Neatness counts Points will be deducted for sloppy work 6 Place answers in the answer blocks provided Be sure to label your answer and include units write F 45 lb not just the number 45 as the answer 7 Individual calculators only Sharing of calculators is prohibited Problem 1 20 A stainless steel pipe with an outside diameter of 120 mm and a wall thickness of 25 mm is rigidly attached to fixed supports at A and B as shown If the length of the pipe is 12 m determine the minimum temperature increase that will cause the pipe to buckle B L A Effective Buckling End Length Supports 1 0 Both Pinned 0 5 Both Fixed One Fixed One Free 2 0 One Pinned One Fixed 0 7 Problem 2 20 A thin membrane is subjected to the plane stress state shown below a Draw the Mohr s circle for this stress state b Identify the in plane principal stresses and maximum in plane shear stress on the Mohr s circle Calculate the values for these stress quantities c Sketch the in plane principal stresses oriented with respect to the y xy coordinate system d Calculate the magnitude of absolute maximum shear stress 160 MPa 300 MPa 150 MPa x y c principal stress state sketch x a Principal Stresses b Maximum in plane Shear Stress d Absolute maximum shear stress Problem 3 20 A stepped 6061 T6 aluminum shaft consists of a solid 4 in diameter segment AB and a solid 3 in diameter segment BC The angle of rotation at C is limited to 8 0 and allowable shear stress for any point on the shaft is 16 ksi Determine the magnitude of the largest torque T that may be applied at C as shown A correct FBD showing internal torque is required for full credit 2 ft 3 ft A B T C Problem 4 20 An aluminum 2014 T6 beam supported by a pin and a roller is shown below The cross section of the beam is a channel section as shown a Draw complete shear and moment diagrams in the space provided under the beam diagram b Determine the maximum values of the tensile and compression stresses in the beam To help you get started the reactions at A and B are 250 lb and 300 lb respectively and the distance from the base of the beam to the neutral axis is y 1 17 inches 10 lb in 150 lb B 4000 lb in A 40 20 10 15 3 4 y 3 3 4 4 Cross Section Maximum Tensile Stress Maximum Compressive Stress Problem 5 20 5 1 List the boundary conditions you would use if you were calculating the deflections for the beam in problem 4 A 10 lb in 4000 lb in 150 lb B 5 2 Calculate the normal strain in the x direction for the stress state in problem 2 if the 20 10 15 40 x membrane is made of Kevlar 49 160 MPa 5 3 Given that for force applied to the bar is F 40 lb calculate the average shear stress in the pin holding the bar to the wall at A The pin has a cross sectional area of 0 25 in2 y x 300 MPa 150 MPa F 5 4 Calculate and sketch the internal loads acting on the beam at the centroid of section A A 30 lb 15 in 20 lb 10 in 4 in A A