lOMoARcPSD|25458655 1593946554 SWK210 EXAM Revision Questions Memo 2020 Strength of Materials 210 (University of Pretoria) Studocu is not sponsored or endorsed by any college or university Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 Turning Point Tutors cc Achieving academic excellence EXAM REVISION SWK210 MEMO Author: Mbali Peloyahae Latest revision date: 25/06/2020 0 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Contents Theme 1 ........................................................................................................................................... 3 Question 1 ................................................................................................................................... 3 Question 2 ................................................................................................................................... 5 Question 3 ................................................................................................................................... 6 THEME 2............................................................................................................................................ 8 Question 4 ................................................................................................................................... 8 Question 5 ................................................................................................................................. 10 Question 6 ................................................................................................................................. 12 Question 7 ................................................................................................................................. 14 THEME 3.......................................................................................................................................... 16 Question 8 ................................................................................................................................. 16 Question 9 ................................................................................................................................. 19 Question 10 ............................................................................................................................... 21 THEME 4 + THEME 5 ....................................................................................................................... 23 Question 11 ............................................................................................................................... 23 Question 12 ............................................................................................................................... 26 Question 13 ............................................................................................................................... 28 Question 14 ............................................................................................................................... 29 Question 15 ............................................................................................................................... 34 Question 16 ............................................................................................................................... 37 Question 17 ............................................................................................................................... 39 Question 18 ............................................................................................................................... 41 Theme 6 + THEME 5 ....................................................................................................................... 43 Question 19 ............................................................................................................................... 43 Question 20 ............................................................................................................................... 46 Question 21 ............................................................................................................................... 49 Question 22 ............................................................................................................................... 51 Question 23 ............................................................................................................................... 53 THEME 7.......................................................................................................................................... 56 Question 24 ............................................................................................................................... 56 Question 25 ............................................................................................................................... 58 Question 26 ............................................................................................................................... 60 Question 27 ............................................................................................................................... 62 1 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 28 ............................................................................................................................... 65 Question 29 ............................................................................................................................... 67 Question 30 ............................................................................................................................... 69 Formula Sheet ................................................................................................................................ 71 References ..................................................................................................................................... 72 2 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Theme 1 Question 1 Marks: [4] The rigid beam BCD is attached by steel bolts to a control rod at B and to a hydraulic cylinder at C. The bolt diameters are ∅π΅ = 16 mm and ∅πΆ = 21 mm. The ππππππ€ of steel is 95 MPa. The metal rod AB has a diameter of 15 mm and the allowable tensile stress of this material is 150 MPa. If the Factor of Safety of this assembly is 2.5, find the ultimate force that can be at C. Solution: 3 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 4 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 2 Marks: [6] The acrylic rod is 350 mm long and 23 mm in diameter, with and applied axial load of 450 N. Determine the change in length and change in diameter of the rod if E = 3 GPa and ν = 0.43. Solution: 5 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 3 Marks: [8] The rigid bar is supported by the pin-connected rod that has a cross-sectional area of 450 mm2 and is made of steel. 3.1 Determine the change in length and the strain of the rod BC. 3.2 Determine the vertical displacement of the bar at B when the load is applied as shown. Esteel = 201 GPa. Solution: 6 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 7 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 THEME 2 Marks: [6] Question 4 The steel pipe is filled with concrete and is subjected to a compressive force P. The pipe has an inner and outer radius of 175 mm and 200 mm, respectively. Est = 202 GPa and Ec = 30 GPa. 4.1 Determine the maximum force P that can be applied if the allowable normal stress in the steel and concrete is 56 MPa and 15 MPa, respectively. What the forces in the steel and in the concrete? 4.2 What is the displacement of the pipe and concrete due to the force P? 4.3 What is the strain in the steel and concrete? Solution: 8 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 9 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [8] Question 5 The figure shows a long section through a circular pipe A with an outside diameter of 55 mm and a wall thickness of 4 mm. The circular pipe A surrounds a solid cylinder B with a diameter of 37 mm. Both the pipe and the cylinder are fixed at C and the pipe is welded to a thin rigid flat circular plate at D. At room temperature [26 °πΆ], the solid bar B is 0.15 mm shorter than the circular pipe A. ∝π¨ = 10 × 10−6 /°πΆ ∝π© = 25 × 10−6 /°πΆ EA = 183 GPa EB = 145 GPa 5.1 What are the normal stresses in the pipe and cylinder, when the temperature is increased so that the cylinder touches the pipe? 5.2 What are the normal stresses in the pipe and cylinder when the temperature is increased to 75 °πΆ? Solution: 10 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 11 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 6 Marks: [8] Three flat steel sheets are fixed by means of a steel rivet by heating the rivet to 735 °πΆ and then placing the rivet through the steel plates as shown. Esteel = 201 GPa πΆππ = 13 × 10−6 /β 6.1 What is the normal stress in the rivet at a temperature 10 °πΆ 6.2 Assume that the two outer sheets are fixed at A. If the diameter of the rivet is 8 mm and a force F of 16 kN acts through the centre of the middle sheet, what is the shear stress in the rivet? 6.3 Assume that t = 16 mm. What is the bearing stress in the middle sheet? 6.4 What is the governing factor for the force F? What is the maximum force F that can be applied? Solution: 12 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 13 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [4] Question 7 Est = 203 GPa Ebr = 105 GPa ECu = 135 GPa Ast = 250 mm2 Abr = 400 mm2 ACu = 520 mm2 ∝ππ = 13 × 10−6 /β ∝ππ = 23 × 10−6 /β ∝πͺπ = 20 × 10−6 /β At an initial temperature of 15°πΆ, there is a 2.5 mm gap between the copper section and the wall. What are the reactions at the fixed ends when the temperature is raised to 50 °πΆ? Solution: 14 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 15 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 THEME 3 Marks: [6] Question 8 The assembly shown consists of a solid rod which is 25 mm in diameter and is fixed to the inside of a tube using a rigid disk at B. The tube has an outer diameter of 53 mm and a wall thickness of 5 mm. The torques applied on the segments AC and BD are as shown in the sketch. G = 85 MPa. 8.1 Determine ππ΄π΅ , ππ΅πΆ , ππΆπ· and ππ΄π· . 8.2 What is the maximum shear stress in the tube and the rod? Solution: 16 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 17 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 18 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [8] Question 9 The solid shaft DF has a diameter of 37 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 36 kW of power to the shaft while turning at 75 revs/s. If gears A, B and C remove 8 kW, 12 kW and 16 kW, respectively, determine the maximum shear stress in segments AB and CF. Solution 19 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 20 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 10 Marks: [8] The composite shaft with length L = 450 mm is manufactured by shrink-fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameters of the two parts d1 and d2 are 35 mm and 41 mm, respectively. The shear moduli of elasticity for the brass and the steel are 33 GPa and 105 GPa, respectively If a constant torsion of 1360 N.m is applied to the shaft, find the shear stress in the brass core and the steel sleeve. Solution: 21 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 22 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 THEME 4 + THEME 5 Marks: [7] Question 11 Set up the discontinuity functions (Macaulay) and draw the shear force and bending moment diagrams for the following beams: 11.1 11.2 11.3 23 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 11.4 Solution: 24 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 25 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [8] Question 12 The aluminium strut has a cross-sectional area in the form of a cross. If it is subjected to a moment of 10.5 N.m, determine the normal stress and shear stress at A and B. Show the results on a stress element. Solution 26 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 27 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 13 Marks: [5] A box beam is constructed from four pieces of wood, glued together as shown. If the moment acting on the beam is 12.36 kNm, determine the normal and shear stresses at A and B. Show the stresses on a stress element. Solution 28 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [18] Question 14 A light beam ABCD is supported by a hinge at B and a roller at C. A uniformly distributed load of 136 kN/m acts between B and C and a point load of 20 kN acts at D. The cross-section of the beam is as shown. 14.1 Calculate the stresses at E – 750 mm to the right of B and 80 mm from the bottom of the cross-section. 14.2 Indicate the stresses on a stress element. 14.3 Determine the principle stresses at E and indicate them on a properly oriented element. 14.4 Determine the maximum shear stress and associated normal stress and indicate them on a properly oriented element. 14.5 Determine the state of stress at E when it is rotated 23° clockwise Solution: 29 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 30 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 31 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 32 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 33 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [10] Question 15 The figure ABC shows a beam that is supported by a hinge at B and a chain at C. The beam acts as a cable bridge to support cables from building A to building C. The given loads include the beams own weight, the cables and the workmen. 15.1 Calculate the maximum tensile, compression and shear stresses. 15.2 Draw the shear stress distribution diagram, with captions, no values necessary Solution: 34 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 35 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 36 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 16 Marks: [4] Given the box-beam ABC, put together with 5.2 mm diameter nails, spaced at 95 mm. 16.1 If the allowable shear stress in the nails is 125 MPa, find the maximum force P that can be applied to the beam Solution: 37 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 38 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [6] Question 17 The composite beam is made of Aluminium (A) and Brass (B). the moduli of elasticity for the aluminium and brass are 72 GPa and 105 GPa, respectively. 17.1 Determine h, the height of the brass strip, so that the neutral axis of the beam is located at the seam of the two metals. 17.2 What is the maximum moment that can be applied if the allowable bending stress in the aluminium is 135 MPa and 30 MPa for the brass? Solution: 39 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 40 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 18 Marks: [6] The T-beam is nailed together as shown. If the nails can each handle a shear force of 3.5 kN, determine the maximum shear force V that the beam can handle, and the corresponding maximum spacing s (to the nearest 5 mm), if the allowable shear stress for timber is 6.5 MPa. Solution: 41 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 42 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Theme 6 + THEME 5 Question 19 Marks: [4] The given I-beam is built in and a horizontal load P acts on the beam as shown. 19.1 Given that a compressive stress may not exceed 75 MPa, determine the largest permissible load P. 19.2 Determine the principle stresses and show them on a properly oriented element. 19.3 Determine the maximum shear stresses and show them on a properly oriented element. Solution: 43 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 44 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 45 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 20 Marks: [6] The figure shows an angle iron with a force F = 1350 kN applied to the angle iron at the position shown. The line of action of F is parallel to the x-axis. 20.1 Determine the state of stress at the point P. Show these stresses on a stress element. Solution: 46 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 47 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 48 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [6] Question 21 A cylindrical pressure vessel is constructed from a long, narrow steel plate by wrapping the plate around a mandrel and then welding along the edges of the plate to make a helical joint. The weld makes an angle of 65° with the longitudinal axis. The vessel has an inner diameter 2.7 m and a wall thickness of 30 mm. The elastic modulus of the material is 205 GPa and ν = 0.33. The internal pressure p is 655 kPa. 21.1 What are the circumferential and longitudinal stresses of the vessel? 21.2 What are the maximum in-plane and out-ofplane shear stresses? 21.3 What are the circumferential and longitudinal strains? 21.4 What is the normal and shear stress acting perpendicular and parallel to the weld seam? Solution: 49 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 50 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 22 Marks: [6] A spherical tank with a diameter of 650 mm is used to store a gas at a pressure of 45 350 kPa. The tank has a yield stress in tension of 1050 MPa, a yield stress in shear of 560 MPa, a modulus of elasticity of 211 GPa, and a Poisson’s ratio of 0.25. The desired factor of safety with regards to yielding is 2.8. and the maximum allowable normal strain is 1360 x 10-6. 22.1 Determine the minimum permissible thickness of the tank. 22.2 If the thickness is 10 mm and the normal strain is 1002 x 10-6, what is the internal pressure in the tank? Solution: 51 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 52 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 23 Marks: [6] The solid shaft is subjected to a torque, bending moment and shear force as shown. The diameter of the shaft is 68 mm. 23.1 Determine the principle stresses at A. 23.2 Determine the principle stresses at B. Solution: 53 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 54 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 55 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 THEME 7 Marks: [6] Question 24 The light beam ABC is supported by a hinge at A and a roller at B. Determine the maximum deflection of the beam in mm. E = 17 GPa and I = 5.2 x 10-6 m4 Solution: 56 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 57 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [6] Question 25 The beam ABC is supported by a hinge at A and a roller at B. Determine the maximum deflection in section AB of the beam. E = 205 GPa and I = 360 v 10-6 m4 Solution: 58 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 59 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [6] Question 26 Determine the maximum deflection of the beam in mm. E = 35 GPa and I = 420 x106 mm4 Solution: 60 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 61 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [6] Question 27 The beam ABC is fixed at A and has a vertical support at B. 29.1 Calculate the vertical deflection of point C. 29.2 Determine the reactions of the beam if the support at B moves 1.5 mm upwards. Solution: 62 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 63 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 64 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [6] Question 28 The beam ABCDE is fixed at A, has an internal hinge at B and has a roller at D. 30.1 Determine the rotation at hinge B. 30.2 Determine the deflection at hinge B. 30.3 Determine the maximum deflection in span BE. Solution: 65 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 66 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Question 29 Marks: [6] A steel beam is fixed at A and is supported by a rod at B. If it is required that the allowable normal stress for the steel is 145 MPa and the maximum deflection does not exceed 1.2 mm, determine the smallest diameter rod that should be used. Est = 213 GPa Solution: 67 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 68 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Marks: [6] Question 30 The simply supported beam is subjected to a constant distributed load as shown and is also supported by a roller at B. Find all the reactions. EI = 100 kNm2 Solution: 69 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 70 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 Formula Sheet THEME 7 TABLES CAN BE FOUND AT THE END OF THE COURSE NOTES! 71 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com) lOMoARcPSD|25458655 © Turning Point Tutors 2020 References GOODNO, B. J., & GERE, J. M. (2018). Mechanics of materials. HIBBELER, R. C. (2017). Statics and mechanics of materials. Upper Saddle River, N.J., Pearson Prentice Hall. 72 Downloaded by Jordan J (jordanjansenvanvuren08@gmail.com)
