Note: - In each project an explanation and general equations should be given. Fields of applications with illustrative pictures. O6U MTE 108– Stress Analysis Project # 1: Stress Analysis of Axial members May, 2020 The horizontal rigid beam ABCD is supported by vertical bars BE and CF and is loaded by vertical forces P1 = 400 kN and P2 = 360 kN acting at points A and D, respectively (see figure). Bars BE and CF are made of steel (E = 200 GPa) and have cross-sectional areas ABE = 11,100 mm2 and ACF = 9,280 mm2. Bars BE and CF have thickness of 37 mm and 32mm respectively. The distances between various points on the bars are shown in the figure. A 10-mm-diameter pin is used at C and 8-mm-diameter pins are used at B and E. The ultimate normal stress is 400 MPa in link BE and CF. Required: a) Draw the free-body diagram of the link ABC, and then calculate reactions at B and C. b) Calculate the axial stresses in the link BE and link CF far from Points B and C. c) Calculate the axial stresses in the link BE and link CF at Points B and C. d) Calculate the axial stain in links BE and CF. e) Take Poisson’s ratio ν= 0.3, calculate the increase in the width of links BE and CF. f) Determine the safety factor of links BE and CF at Pins B and C. g) Determine the vertical displacements δA and δD of points A and D, respectively. O6U MTE 108 – Stress Analysis Project # 2 : Stress Analysis of Shear members May, 2020 Solve two problems Problem #1: An angle bracket having thickness t=12.7mm is attached to the flange of a column by two 16 mm diameter bolts (see figure). A uniformly distributed load acts on the top face of the bracket with a pressure p=2 MPa. The top face of the bracket has length L=152 mm. and width b=63 mm. Determine the average bearing pressure σb between the angle bracket and the bolts and the average shear stress aver in the bolts. (Disregard friction between the bracket and the column.) Problem#2: A bolted connection between a vertical column and a diagonal brace is shown in the figure. The connection consists of three 16 mm bolts that join two 6 mm end plates welded to the brace and a 16 mm gusset plate welded to the column. The compressive load P carried by the brace equals 8.0 k. Determine the following quantities: (a) The average shear stress τaver in the bolts, and (b) The average bearing stress σb between the gusset plate and the bolts. (Disregard friction between the plates.) Problem #3: A steel plate of dimensions 2.5 x 1.2 x 0.1 m is hoisted by a cable sling that has a clevis at each end (see figure). The pins through the clevises are 18 mm in diameter and are located 2.0 m apart. Each half of the cable is at an angle of 32° to the vertical. For these conditions, determine the average shear stress τaver in the pins and the average bearing stress σb between the steel plate and the pins. O6U MTE 108 – Stress Analysis Project # 3 : Stress Analysis of Trusses May, 2020 The rigid bar EFG is supported by the truss system shown. Knowing that the members AE, AB, BF, BC, CF, CG, and DE are solid circular rods of 17 mm. Using E=70Gpa. a) Determine the ground reactions at A and D of structure. b) Check the determinacy of the structure. c) Determine the internal forces in the members using Joint Equilibrium method. d) Determine the vertical deflection of point F caused by the applied load. e) Determine the internal forces in members AE, AB and DE using the method of sections O6U MTE 108 – Stress Analysis Project # 4 : Stress Analysis of Torsional members May, 2020 Two solid shafts (G=77 GPa) are connected by gears shown. A toque of magnitude T=1000 N.m is applied at D as shown. Knowing that the diameter of shaft AB is 56 mm and the diameter of shaft CD is 42 mm. The gear C radius is 40 mm and the gear B radius is 100mm. The shaft CD length LCD= 500mm and the shaft AB length is LAB=400mm determine: a) The maximum shearing stress in shaft AB and shaft CD. b) The angle of twist in shaft AB and shaft CD. c) The total angle of twist at D. O6U MTE 108 – Stress Analysis Project # 5 : Stress Analysis of Beams May, 2020 The beam in the figure below is subjected to 10kN and 15kN vertical forces at points A and E, uniformly distributed load with density 10kN/m. The cross-section of the beam is shown to the right. Its dimensions are in mm. a) Determine the reactions at the supports C and B. b) Draw the Shear Force Diagram and Bending Moment Diagram. c) Determine the cross-section area, the neutral axis and the second moment of area about the neutral axis NA. d) Calculate the stress due to bending at the point having maximum bending moment. Plot the stress distribution through the cross-section. e) Knowing that the allowable stress of the beam-material is allow = 150 GPa, is the beam safe or not. If safe, determine the safety factor.