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- Determine the maximum tensile bending stresses in the beam shown. LetP= %3D 19 Note Answer in whole number I = 100 × 106 mm4 P kN/m 2. NA 130 mm 6 m B = 4P 200 mm 2P kN 6-X= Am 4P : - GPA thin polymer plate PQR is deformed so that corner Q is displaced downward by a distance L = 1.45 mm to new position Q' as shown. Determine the shear strain at Q' associated with the two edges (PQ and QR). 120 mm 480 mm. P R 240 mm -2692 μrad -3352 μrad O-4917 prad -3610 μrad O-2921 urad Q 'Q' XW A L A Test beam Strain gauge (a) Unsymmetrical cantilever beam with weight applied at the free end and at the "shear centre", so that there is no torsion induced. b Section A-A Strain gauge 1 Strain gauge 3 Strain gauge 2 B (b) Location of Huggenberger strain gauges a D Referring to the above figure, calculate the location of the centroid, the second moments and product of area for the cross-section if; • D = 67 mm • B = 41 mm • t = 2.41 mm. From these, calculate the position and orientation of neutral axis for pure bending in the vertical plane (i.e. bending about a horizontal axis). Also calculate the directions of the principal second moments of area. Next, graph as scale diagram of the cross-section and plot the neutral axis on that diagram in the correct location and indicate the direction of deflection for the same conditions
- ! Required information Consider the given state of stress. to A16 ksi 10 ksi Determine the normal and shearing stresses after the element shown has been rotated through 10° counterclockwise, using Mohr's circle. The normal stress ox'is ksi and oy'is |ksi. The shear stress Tx'y'is ksi.Problem 2 The rigid bar is plnned at A and held by two flexible bars at E and C. The load P Is applled at B. The two flexible bars FE and DC each have a diameter of 1 In. The flexible bars are elastic- perfectly plastic with a yleld stress equal to 20 ksl and a yleld strain of 0.001. Determine the following: The load R, at first yleld and the corresponding deflection at B, &, The ultimate load Pu and the corresponding deflection du The permanent deflection and residual stresses in each rod if the ultimate load is removed Construct P - A curve showing yield, ultimate and permanent deformation o (ksi) 1 ft E F 1 ft1 ft 20 B P e (in./in.) 0.001 1 ft D 2 ft 1 ft AThe shaft is made from a solid steel section AB and a tubular portion made of steel and having a brass core. If it is fixed to a rigid support at A, and a torque of T 50 lb.ft is applied to it at C, determine the rotation angle that occurs at C relative to A and compute the maximum shear stress and maximum shear strain in the brass and steel. Take Gst = 11500 ksi, Gbr 5600 Ksi. %3D %3D 3 ft 2 ft 0.5 in. 1 in. T = 50 lb ft
- Detemine the principal stress acting at point B, which is located just on the web, below the horizontal segment on the cross section Show the results on a properly oriented element located at this point. Although it is not very accurate, use the shear formula to calculate the shear stress. -AO mm- 300 mm 150 mm 12 mm 130 mim 15 mm 6 kNAs shown in the figure, aluminum, E= 70GPa links (1) and (2) support rigid beam ABC. Link (1) has a cross-sectional area of 320mm² and link (2) has a cross-sectional area of 480mm². For an applied load of P= 58kN, determine the rigid beam deflection at point B. (2) 4,000 mm (1) 2,500 mm B 1,400 mm 800 mm2. A finite element analysis of a bearing housing indicates that at a point p, the material is subjected to the state of stress (in MPa): Ox Txy Txz] Txy Oy Tyz Txz Tyz 0₂ 0 -30 -10 -10 40 Determine the principal stresses and the absolute maximum shear stress. [20 20 = 20 0
- W A Test beam A Strain gauge (a) Unsymmetrical cantilever beam with weight applied at the free end and at the "shear centre", so that there is no torsion induced. Section A-A Strain gauge 1 b Strain gauge 3 Strain gauge 2 B (b) Location of Huggenberger strain gauges a Referring to the above figure, calculate the location of the centroid, the second moments and product of area for the cross-section if; • D = 67 mm B = 41 mm t = 2.41 mm. From these, calculate the position and orientation of neutral axis for pure bending in the vertical plane (i.e. bending about a horizontal axis). Also calculate the directions of the principal second moments of area. Next, graph as scale diagram of the cross-section and plot the neutral axis on that diagram in the correct location and indicate the direction of deflection for the same conditions3) The plate shown is fixed connected along AB and held in the horizontal guides at its top and bottom, AD and BC. If its right side CD is given a uniform horizontal displacement of 4 mm, determine (a) the average normal strain along the diagonal AC, and (b) the shear strain at E relative to the x, y axes y. i= 340 mm j= 479 mm D k = 170 mm A k E j k B i 4тmThe rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 519 mm2; link CE is made of steel (E = 200 GPa) and has a cross-sectional area of 619 mm?. For the 41 kN force shown, determine the deflection of B (mm) *deflection should have a negative sign if compression and positive if tension. Also, your final answer should have two decimal places 04 m 0.3 m E 0.4 m 0.2 m