Eleventh Edition 6 CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P

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Eleventh Edition 6 CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. David F. Mazurek Analysis of Structures Copyright © McGraw-Hill Education. Permission required for reproduction or display. Eleventh Edition Vector Mechanics for Engineers: Statics Example 6.13 (Method of Joints) Using the method of joints, determine the force in each member of the roof truss shown. State whether each member is in tension or compression. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-2 Eleventh Edition Vector Mechanics for Engineers: Statics Example 6.43 (Method of Sections) A Mansard roof truss is loaded as shown. Determine the force in members DF, DG, and EG. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-3 1 Eleventh Edition Vector Mechanics for Engineers: Statics Example 6.128 (Force transmission) The press shown is used to emboss a small seal at E. Knowing that the vertical component of the force exerted on the seal must be 900 N, determine (a) the required vertical force P, (b) the corresponding reaction at A. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-4 Eleventh Edition Vector Mechanics for Engineers: Statics Example 6.155 (Force transmission) The telescoping arm ABC is used to provide an elevated platform for construction workers. The workers and the platform together have a mass of 200 kg and have a combined centre of gravity located directly above C. For the position when θ= 20o, determine (a) the force exerted at B by the single hydraulic cylinder BD, (b) the force exerted on the supporting carriage at A. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-5 2 PROBLEM 6.13 Using the method of joints, determine the force in each member of the roof truss shown. State whether each member is in tension or compression. SOLUTION Free body: Truss: 6Fx 0: A x Ay E Ay E 3.6 kN 0 From symmetry of loading: 1 2 total load We note that DF is a zero-force member and that EF is aligned with the load. Thus, FDF FEF 0W 1.2 kN C W Free body: Joint A: FAB 13 FAC 12 2.4 kN 5 FAB 6.24 kN C W FAC 2.76 kN T W Free body: Joint B: 6Fx 0: 6 Fy 0: 3 12 12 FBC FBD (6.24 kN) 0 3.905 13 13 2.5 5 5 FBC FBD (6.24 kN) 2.4 kN 3.905 13 13 (1) 0 Copyright © McGraw-Hill Education. Permission required for reproduction or display. (2) PROBLEM 6.13 (Continued) Multiply Eq. (1) by 2.5, Eq. (2) by 3, and add: 45 45 FBD (6.24 kN) 7.2 kN 13 13 0, FBD 4.16 kN, FBD 4.16 kN C W 0, FBC 2.50 kN, 2.50 kN C W Multiply Eq. (1) by 5, Eq. (2) by –12, and add: 45 FBC 28.8 kN 3.905 FBC Free body: Joint C: 6Fy 0: 5 2.5 FCD (2.50 kN) 0 5.831 3.905 6Fx 0: FCE 5.76 kN FCD 1.867 kN T W 3 3 (2.50 kN) (1.867 kN) 3.905 5.831 FCE 0 2.88 kN T Free body: Joint E: 6Fy 0: 5 FDE 3.6 kN 1.2 kN 7.81 FDE 6Fx 0: FCE FCE 0 3.75 kN FDE 3.75 kN C W 6 (3.75 kN) 0 7.81 2.88 kN FCE 2.88 kN T (Checks) Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 6.43 A Mansard roof truss is loaded as shown. Determine the force in members DF, DG, and EG. SOLUTION Reactions: Because of the symmetry of the truss and loadings, Ax 0, Ay L 1 (1.2 kN) 5 2 3 kN We pass a section through DF, DG, and EG and use the free body shown: Member DF: 6M G FDF 0: (1.2 kN) 8 m 1.2 kN 4 m 3 kN 10.25 m FDF (3 m) 5.45 kN 0 5.45 kN C W FDF Member DG: Member EG: 6M D 0: 6Fy §3· 0: 3 kN 1.2 kN 1.2 kN ¨ ¸ FDG ©5¹ FDG 1.000 kN FDG 0 1.000 kN T W 1.2 kN 4 m FEG (3 m) (3 kN)(6.25 m) 0 FEG 4.65 kN T W Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 6.128 The press shown is used to emboss a small seal at E. Knowing that the vertical component of the force exerted on the seal must be 900 N, determine (a) the required vertical force P, (b) the corresponding reaction at A. SOLUTION FBD Stamp D: 6Fy 0: 900 N FBD cos 20q 0, FBD 957.76 N C (a) FBD ABC: 6M A (b) 6Fx 6Fy 0: [(0.2 m)(sin 30q)](957.76 N)cos 20q [(0.2 m)(cos30q)](957.76 N)sin 20q [(0.2 m)sin 30q (0.4 m) cos15q]P 0: Ax (957.76 N)sin 20q 0 P 0: Ay (957.76 N) cos 20q 301.70 N 0 P 302 N W 301.70 N, Ax 327.57 N 0 Ay A 682 N 598.30 N 61.3° W Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 6.155 The telescoping arm ABC is used to provide an elevated platform for construction workers. The workers and the platform together have a mass of 200 kg and have a combined center of gravity located directly above C. For the position when T 20q, determine (a) the force exerted at B by the single hydraulic cylinder BD, (b) the force exerted on the supporting carriage at A. SOLUTION Geometry: a b c (5 m) cos 20q 4.6985 m (2.4 m) cos 20q 2.2553 m (2.4 m)sin 20q 0.8208 m d b 0.5 1.7553 m e c 0.9 1.7208 m tan E e d 1.7208 ; E 1.7553 44.43q Free body: Arm ABC: We note that BD is a two-force member. (a) (b) 6M A W (200 kg)(9.81 m/s 2 ) 1.962 kN 0: (1.962 kN)(4.6985 m) FBD sin 44.43q(2.2553 m) FBD cos 44.43(0.8208 m) 0 9.2185 FBD (0.9927) 0: FBD 6Fx 6Fy 0: Ax FBD cos E Ax 9.2867 kN FBD 44.4q W 0 (9.2867 kN)cos 44.43q 6.632 kN 0: Ay 1.962 kN FBD sin E Ay 9.29 kN 0 1.962 kN (9.2867 kN) sin 44.43q Ax 6.632 kN 4.539 kN Ay A 8.04 kN 4.539 kN 34.4q W Copyright © McGraw-Hill Education. Permission required for reproduction or display. Eleventh Edition 4 CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. David F. Mazurek Equilibrium of Rigid Bodies Copyright © McGraw-Hill Education. Permission required for reproduction or display. Eleventh Edition Vector Mechanics for Engineers: Statics Example 4.15 Two links AB and DE are connected by a bell crank as shown. Knowing that the tension in lin AB is 720 N, determine(a) the tension in link DE, (b) the reaction at C. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-2 Eleventh Edition Vector Mechanics for Engineers: Statics Example 4.46 Knowing that the tension in wire BD is 1300 N, determine the reaction at the fixed support C of the frame shown. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-3 1 Eleventh Edition Vector Mechanics for Engineers: Statics Example 4.117 A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over a frictionless hook at C. Assuming that the tension is the same ion both part of the cable, determine (a) the tension in the cable, (b the reactions at A and B. Assume that the hinge at B does not exert any axial thrust. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-4 Eleventh Edition Vector Mechanics for Engineers: Statics Example 4.150 A 200-mm lever and a 240-mm-diameter pulley are welded to the axle BE that is supported by bearings at C and D. If a 720-N vertical load is applied at A when the lever is horizontal, determine (a) the tension in the cord, (b) the reactions at C and D. Assume that the bearing at D does not exert any axial thrust. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-5 2 Eleventh Edition 5 CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. David F. Mazurek Distributed Forces: Centroids and Centers of Gravity Copyright © McGraw-Hill Education. Permission required for reproduction or display. Eleventh Edition Vector Mechanics for Engineers: Statics Example 5.1 Locate the centroid of the plane area shown. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-2 Eleventh Edition Vector Mechanics for Engineers: Statics Example 5.36 Determine by direct integration the centroid of the area shown. Express your answer in terms of a and h. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-3 1 Eleventh Edition Vector Mechanics for Engineers: Statics Example 5.66 For the beam and loading shown, determine (a) the magnitude and location of the resultant of the distributed load, (b) the reactions at the beam supports. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-4 Eleventh Edition Vector Mechanics for Engineers: Statics Example 5.67 For the beam and loading shown, determine (a) the magnitude and location of the resultant of the distributed load, (b) the reactions at the beam supports. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-5 2 Eleventh Edition 7 CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. David F. Mazurek Internal Forces and Moments Copyright © 2013 McGraw-Hill Education. Permission required for reproduction or display. Eleventh Edition Vector Mechanics for Engineers: Statics Example 7.19 Knowing that the radius of each pulley is 200 mm and neglecting friction, determine the internal forces at Point J of the frame shown. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 7- 2 Eleventh Edition Vector Mechanics for Engineers: Statics Example 7.36 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-3 1 Eleventh Edition Vector Mechanics for Engineers: Statics Example 7.39 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-4 Eleventh Edition Vector Mechanics for Engineers: Statics Example 7.30 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment. Copyright © McGraw-Hill Education. Permission required for reproduction or display. 2-5 2 ENS1101D – Assignment – problem sets (20%) Instructions Submit four separate examples from week 4, week 5, week 6 and week 7. The examples must be unique, not published or presented elsewhere or by someone else and written in MS WORD. It must be YOUR OWN WORK, the pictures and diagrams inserted in the MS WORD MUST be unique, not published elsewhere and completed in the PowerPoint. Structure Each example MUST have the following structure/headings: 1. Title: Week 3 - ……… 2. What is given 3. What theoretical concepts have been applied 4. Detailed and well annotated diagrams (force diagrams, free body diagrams etc.) drawn in the PowerPoint and workings with explanation. Handwritten drawings will be not accepted. 5. Demonstrate that you are able to think critically: If you change one value in your workings (e.g., load, support, dimension) explain what is the outcome of this change and what should be done to avoid failure. What do I need to submit? Submit four completed examples from weeks 4, 5, 6 and 7 in MS Word via Turnitin link provided on Moodle. The Turnitin will check for the originality of your work. Any workings that will be found on the internet or elsewhere will receive zero and will be reported to ECC Academic Integrity officer for further investigation. Submit your original PowerPoint file that contains all pictures and diagrams How many files? Two files. One MS Word file that contains four completed questions, and one PowerPoint file that contains your original pictures and diagrams. What types of files you can submit? MS Word and PowerPoint General Marking Turn-Around There is a 2-week turnaround to upload the marks and provide global feedback. Students can receive a maximum of 10 marks for each question, ie. 40 marks in total. There are 4 questions in total. Each question carries 5% weighting, 20% in total. General marking guide Marking Criterion Structure correctly followed 1. Title 2. Given 3. Theory 4. Diagrams and workings 5. Critical thinking Correct diagrams and workings Critical thinking Marks 4 4 2 Note: The above marks are subject to the original PowerPoint file that must be submitted with your workings. Failure to do so will result in zero mark. Workings, diagrams or pictures must be unique and be created by yourself in PowerPoint. Failure to do so will result in zero mark and will be investigated by the Academic Integrity Officer. FORMULAE SHEET 1. DERIVATES 4. CENTROIDS !" # = %" #&' !" x= !()*) !* !) =) + * !" !" !" y= = ò xdA ò dA Qx = A ò ydA ò dA Qy A ) ! .* / !) !* * !" − ) !" = !" *1 !23% " = 452 " !" !452 " = −23% " !" !67%" = 284 1 " !" 2. INTEGRALS 9 " # !" = Composite technique for centroids å xA åA å yA Y = åA X = 5. MOMENT OF INERTIA I x = ò y 2 dA I y = ò x 2 dA " #:' %+1 9 23% " !" = −452 " 9 452" !" = 23% " 3. IMPENDING SLIPPAGE IN FLEXIBLE BELTS