ES230 STRENGTH OF MATERIALS Exam 1 Study Guide. Exam 1: Wednesday, February 8 th, in-class Updated 2/5/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 1. Exam Format: Closed book. The formulae below will be given. Students can expect 20% of the exam to be in the form of conceptual questions, while 80% will be computational. Time Limit: 50 minutes. Given Formulae (these will be found on the exam): Normal stress = F/A, where F is the force that is normal to the cut and A is the area of the cut. Shear stress = V/A, where V is the force that is normal to the cut and A is the area of the cut. LESSON COVERAGE, OBJECTIVES, AND EXAMPLE PROBLEMS: The exam covers Lessons 2 through 5. The objectives are given below, with example problems/questions for each objective. Students are strongly advised to solve as many problems as possible from the Philpot textbook, sections 1.1 to 1.6. In addition to those problems and the problems below, five sample exams with solutions are found on the course webpage. Name the unknown loading resultants that may be present at a cut through a planar body or a three-dimensional body. 1. (3 points) If a cut is taken at Point D, how many unknown internal forces or internal moments are present there? Given: A is a roller support, D is a point midway between A and B, B is a pinned connection, E is a point midway between B and C, C is a fixed support. 2. (3 points) For the previous beam, how many unknowns (internal forces, moments) are present at Point B? 3. (5 points) The previous beam has 4 unknown external reactions, yet is solvable by Statics. Show how these can be solved by Statics. 4. (3 points) What is the internal moment at Point B, for the beam below? 5. (3 points) TRUE or FALSE. For the previous beam, there is no internal shear force present at Point B. 6. (3 points) TRUE or FALSE. For the previous beam, there is not internal moment present in the beam over the roller support C. 7. (3 points) In general, what is the maximum number of unknown internal forces or moments that may be present at a cut of a two-dimensional problem? 8. (3 points) In general, what is the maximum number of unknown internal forces or moments that may be present at a cut of a three-dimensional problem? 9. (3 points) When analyzing the previous beam to determine the external support reactions, explain why it is necessary to cut the structure at point B. 10. (3 points) How many internal unknowns are there at cross-section B?
Solve internal resultant loadings (forces and moments) acting within planar machines and structures by taking cuts and applying equilibrium. 11. (15 points). Determine the internal moment that is present at point A for the beam below and indicate whether this moment causes compression on the top or on the bottom of the beam. Given: Point A is supported by a pin, while Point B is a roller support. 5 kips 5 kips 1 kip/ft A B 5 ft 12 ft 5 ft 12. (15 points). Referring to the previous beam, determine the internal moment that is present midway between A and B and clearly specify its sign. 13. (20 points). Determine the resultant internal loadings (forces and moments) at Point B. Clearly indicate whether the moment causes compression on the top or on the bottom of the beam. Indicate the sign of the shear force by drawing an icon with the forces showing the direction in which the shear acts. Given: The beam has a fixed support at Point A and is free at Point C. 14. (15 points). Determine the internal bending moment at point C and indicate whether this moment causes compression on the left or the right side of the beam.
Recognize two-force members and use this to simplify problems, knowing that internal shear and moment must be zero on the cross-section. 15. (3 points). Explain why the reaction component C y must be zero. 16. (3 points) Determine the internal shear force on the cross-section at the midpoint between B and C, from the previous problem. 17. (3 points) What is the maximum internal bending moment in Member BC, from the previous problem? 18. (3 points) TRUE or FALSE. The cross-section at point F may have internal normal force, but cannot have internal moment or internal shear force. Solve internal resultant loadings for machines or structures when multiple free-body diagrams are needed. 19. (25 points) Determine the resultant internal loadings (forces and moments) on the cross section through point D. Given: Loadings shown. Point B is an internal pinned connection Point A is a roller support Point C is a fixed support
20. (20 points) Determine the resultant internal loadings (forces and moment) on the cross-section through Point I on the drum lifter. Given: The gripping action on the top of the drum has horizontal and vertical force components, only. 21. (30 points) Determine the internal normal force N, the internal shear force V, and the internal moment M at crosssection F, due to the applied loads. For the internal moment, specify whether the moment causes compression on the left or on the right. For the internal normal force, specify whether it is in compression or tension. Given: Member ABC is connected to member CDE by a pin. Pinned supports at A and E Loadings and dimensions as shown. (partial ans: M F = 10.6 kip-ft, compression on the left) 5 kips 5 kips C B 2.5 D 2.5 F 6 6 A E 12 12 22. (40 points) Determine the magnitude of the internal moment M at point F and specify the sign of the internal moment. Given: Member ABFC is a continuous member that is connected to member CDE by a pin at C. There are pinned supports at A and E. There is a uniformly-distributed loading of 1 kip/ft from B to C and a uniformly-distributed loading of 2 kips/ft from C to D.
1 kip/ft 2 kip/ft B F C D 10 ft A E 5 ft 5 ft 10 ft Define normal and shear stress. Determine when the F/A and V/A equations are applicable (instances of uniform stress) and when they are not applicable (instances of non-uniform stress). 23. (3 points) TRUE or FALSE. The maximum normal stress on this beam is equal to P/A. Given: The beam shown has a cross-sectional area of A. P h Area A L/2 L/2 Cross-Section 24. (3 points) TRUE or FALSE. For previous beam, the maximum normal stress on this beam is equal to P/A. 25. (3 points) True or False. For the previous beam, the average shear stress at the left support is equal to P/(2A). Compute normal and shear stresses on uniformly stressed bodies. 26. (20 points) Determine the normal stress a-a and shear stress a-a on cross-section a-a if the cross-sectional area is 1 in 2. D 1000 lb. 1 1 Cross Section of Member AB b a B 6 in. b 6 in. A a C 27. (30 points). For the previous problem, determine the normal and shear stresses on cut b-b. 28. (40 points). If the maximum allowable normal stress is 20 ksi and the maximum allowable shear stress is 12 ksi, determine the minimum required cross-sectional area for member AB in the truss, below. 8 in.
29. (15 points). A punch press requires 28.27 kips of force to punch out a 1 diameter hole in a piece of ¼ thick steel plate. Determine the shear strength of this type of steel. 30. (20 points). Two 2 x 6 boards are glued to one another and to two 4 x 5 x ½ splice plates, as shown. If the glue has a tensile (normal) strength of 500 psi and a shear strength of 1000 psi, determine the tensile force P that will cause the glued joint to fail if the tensile and shear surfaces fail simultaneously (i.e., tensile and shear surfaces both reach their ultimate strengths at the same time). 4 4 x 5 x ½ Splice Plate P 5 2 P 6 2 x 6 x 12 Boards Glued surfaces 2 31. (20 points). Determine the shear stress on the 3/8 diameter bolts, due to the applied 1000-lb loads, shown.
1000 lbs 1000 lbs 32. (20 points). If the previous 3/8 bolts are inserted into 3/8 holes, determine the bearing stress on the holes in the previous problem. 33. (15 points). A steel plate is fastened to a wooden block using (4) 3/8 diameter lag bolts that are embedded 2.5 into the wood, as shown. If a 5000-lb force is applied to the center of the steel plate, with orientation, as shown, determine the shear stress in a bolt. 4 3 5000-lbs 34. (20 points). Considering the previous problem, determine the average shear stress between the lag bolts and the wood that the lag bolts are embedded in. Assume that all of the force transfer between the bolts and the wood occur in shear. 35. (20 points). A 6x6x½ steel plate is glued to a wooden block and subjected to an inclined force, P, determine the maximum force P that may be applied to the steel plate if the glue stresses must not exceed either 600 psi in shear or 1200 psi in tension.
4 3 P
ANSWERS TO QUESTIONS 1 TO 35 OF THIS GUIDE 1. 3 2. 2 3. 1 st, solve FBD ADB, then solve FBD BEC 4. 0 5. FALSE 6. FALSE 7. 3 8. 6 9. 4 external unknowns are solvable as one FBD, making it necessary to cut at internal pin to solve 2 separate FBD s. 10. 6 11. 25 kip-ft, compression on bottom 12. 7 kip-ft, compression on bottom 13. 1152 kip-ft, compression on bottom 14. 92 kip-ft, compression on left 15. BC is a 2FM. Reaction is horizontal. Cy=0 16. 0. 2FM: V=0 17. 0. 2FM: M=0 18. TRUE 19. M=13.5 kip-ft (compression on top). V = 0.75 kips (positive) 20. N=250 lbs (T), V= 144.3 lbs, M=1155 ft-lb (compression on left) 21. N=5kips, V=30/17 kips, M=180/17 kip-ft (compression on left) 22. 25 kip-ft, compression on bottom 23. FALSE 24. FALSE 25. TRUE 26. aa=2500psi (T), aa=0 27. aa=1600psi (T), aa=1200psi 28. 0.431 in 2 29. 36 ksi 30. 26 kips 31. 12.0 ksi 32. 7.07 ksi 33. 6.79 ksi 34. 340 psi 35. 36 kips (shear controls)