Name E MCH 213 Strength of Materials Sample FINAL EXAM 2 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 If you need more paper to keep your work organized just ask 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 or taken from a shear moment 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 set of stilts has been constructed from 2 in by 4 in boards made of Douglas Fir as shown The wide foot at the bottom of each stilt creates a fixed condition while the top end is essentially free If these stilts are 10 ft long and are designed to support a person weighing up to 180 lbs determine the magnitude of the largest axial deformation each stilt will experience and the factor of safety with respect to buckling Please note that as the person is walking he or she must balance on a single stilt Effective Buckling End Length Supports 1 0 L Both Pinned Both Fixed 0 5 L One Fixed One Free 2 0 L One Pinned One Fixed 0 7 L Max Deformation Factor of Safety Problem 2 25 A motor attached to the A36 Steel shaft at C drives two mechanisms at A and B Determine the maximum value of T such that the shear stress in the shaft does not exceed 18 ksi and the rotation of end A with respect to end C does not exceed 5 degrees AB is hollow with an inner diameter of 2 in and an outer diameter of 3 in and BC is solid with a diameter of 2 5 in 5 ft 4 ft 3T T A B 4T C T max Problem 3 25 You are designing a cylindrical cardboard tube to hold biscuit dough that will experience an internal pressure of 2 psi a 3 lb axial load and an 9 in lb torque as shown The tube has an outer radius of 1 5 in a wall thickness of 0 1 in and a length of 7 in a Determine the state of stress at point A on the outer surface due to these loads and sketch this state of stress on the stress cube provided below b Use Mohr s circle to calculate the principal stresses at point A Sketch the principal stresses on a rotated element and specify the orientation of the element with respect the original x axis 9 in lb 3 lb A y z x a b y A z x Problem 4 20 The beam shown below is free at point A and is clamped built in at point B Determine the deflection at the free end point A Use a bending stiffness EI 15 x 103 kN m2 11 kN A B y x 4 m 5 m v Problem 5 10 5 1 Using the plot shown select the correct concentration factor for a 4 in wide axially loaded bar with a 0 4 in radius hole A 2 0 B 2 1 C 2 2 D 2 3 E 2 4 5 2 For the original 1 mm x 1 mm element deformed as shown select the correct shear strain from the list below A 0 1 rad B 0 1 rad C 0 4 rad D 0 4 rad E 0 5 rad F 0 5 rad G 2 0 1 rad H 2 0 1 rad I 2 0 4 rad J 2 0 4 rad K 2 0 5 rad L 2 0 5 rad 5 3 Using the stress strain curve shown identify the yield stress for this material A 200 MPa B 250 MPa C 370 MPa D 450 MPa E 925 MPa F 1 8 GPa G 200 GPa 5 4 A pressure vessel is fabricated from a plate by butt welding a helix which forms an angle of 65 degrees with the horizontal x axis as shown Once the stresses are known on x and y faces of the element shown what value would you use for in the transformation equations to determine the normal and shear stress on the welded surface A 25 degrees B 25 degrees C 65 degrees D 65 degrees E 115 degrees F 115 degrees G 155 degrees H 155 degrees y 65 0 x