A post is supported by a ball-and-socket joint at O and cables BC and BD. A triangular distributed load runs from O to A as shown and has a maximum intensity of w = 36 N/m Length OA is 1.6 m and length OB is 2.5 m Other dimensions are given: hi = 1.48 m l = 0.89 m ho = 0.97 m l2 = 0.65 m Z C h2 h, 12 A В y W
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- A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 75 lb/ft" against the full area of the sign. The dimensions of the poles and sign are hx= 20 ft, /r =5 ft, and h = 10 ft. To prevent buckling of the walls of the poles, the thickness e is specified as one-tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7500 psi in the aluminum. (b) Determine the minimum required diameter based upon an allowable shear stress of 300 psi.A steel post /t if with a hollow circular cross section is fixed at the base and free at the top (see figure). The in net and outer diameters arc d1= 96 mm and d2= 110 mm, respectively, and the length is L = 4.0 m. A cable CED passes through a fitting that is welded to the side of the post. The distance between the plane of the cable (plane CBD) and the axis of the post is e = 100 mm, and the angles between the cable and the ground arc a = 53.13º. The cable is preten-sioned by tightening the turn buck les. If the deflection at the top of the post is limited to = 20 mm, what is the maximum allowable tensile force Tin the cable? (Assume E = 205 GPa.)Two cables, each having a length i. of approximately 40 m, support a loaded -container of weight W (see figure). The cables, which have an effective cross-sectional area A = 48.0 mm2 and effective modulus of elasticity E = 160 GPa. are identical except that one cable is longer than the other when they are hanging separately and unloaded. The difference in lengths is d = 100 mm. The cables are made of steel having an elastoplastic stress-strain diagram with a r= 500 MPa. Assume that the weight ft' is initially zero and is slowly increased by the addition of material to the container. (a) Determine the weight Wythat lirsl produces yielding of the shorter cable. Also, determine the corresponding elongation 5 of the shorter cable. (b) Determine the weight Wpthat produces yielding of both cables. Also, determine the elongation Spof the shorter cable when the weight W just reaches the value Wp. (c) Construct a load-displacement diagram showing the weight W as ordinate and the elongation
- A mass of 1019Kg is supported by two wires A and B each made of a different material. Before loading the wires are of equal length. After loading they are still of equal length. Find the load carried by each wire. Wire Diameter mm E Nmm-2 A 1 206,000 B 2 116,000A central horizontal section of a hook is a symmetrical trapezium of inner width=67.5mm and of outer width =22.5mm. The depth of the section is 90mm. The hookcarries a load of 37.5kN. The load line passes through the centre of curvature. Theradius of the hook is 52.5mm. Determine the maximum compressive and tensilestresses in the section of the hook.A structural membrane contains surface flaws of initial depth of 0.015 inchesDetermine the life of the membrane in cycles if it is repeatedly loaded from 0 to 60 ksi. Assume K1=95 ksi-in¹/2, n=3 and C=4x10-10 (Ksi²cycle)^-1
- The circular section steel bar bent in L shape is attached to a fixed wall at end A. A force P is applied to the rod in the vertical direction from the free end C. In what range is the safe diameter value of this ductile rod according to Von-Mises criterion? P=3kN, L1=3m, L2=2m, sak= 400MPa, tak= 200MPa, safety factor : n = 2 p = 3A W section is used as a column of hinged ends with a length of 6 m. Fy = 248 MPa and E = 200GPa.Use the formula for combined stress. Section properties:A = 21300 mm2Sx = 2080 x 10^3 mm^3rx = 119 mmSy = 746 × 10^3 mm^3ry = 68.10 mm Questions:Determine the safe distance along the plane of the web could an eccentric load of 197.6 kN be placed.Hint Answers: 1,420.18A horizontal bar, fixed at one end (x = 0), has a length of 1 m. and cross-sectional area of 100 mm2 Its elastic modulus varies along its length as given by E(x) = 100e-x GPa, where is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 KN is applied at the free end (x = 1). The axial displacement of the free end is..... mm
- A rigid bar, AB, is pinned at point B. Two other bars, AC and AD, are connected to point A to provide support for AB. We are investigating the behavior of this system under a specific load. Key Details: Bar properties: Material: Steel with Young's modulus (Esteel) of 200 GPa and coefficient of thermal expansion (a) of 11.7 x 10^-6 /°C. Cross-sectional area: AC: 1960 mm² AD: 1250 mm² Length: AC: √2 meters (square root of 2 meters) AD: 1 meter Inclination angles: AC: θ₁ (theta 1) = 30° from horizontal AD: θ₂ (theta 2) = 20° from horizontal Load on bar AB: Idealized linearly increasing load with a maximum value of 30 kN/m at point B. Problem Objectives: Determine the internal forces (axial forces) acting within bars AC and AD due to the applied load on AB.A device consists of a horizontal beam ABCsupported by two vertical bars BD and CE. Bar CEis pinned at both ends but bar BD is fixed to thefoundation at its lower end. The distance from A toB is 600 mm and from B to C is 350 mm. Bars BDand CE have lengths of 350 mm and 450 mm, respectively,and their cross-sectional area is 720 mm2. Thebars are made of steel having a modulus of elasticityE = 200 GPa. If load P is 20 kN, calculate the displacementat point A.The rigid bar AB with a length of 5m, is attached to two vertical rods and ishorizontal before the uniformly varying load of zero intensity at point A and 10kN/mat point B is applied. The rod at A is steel with L=3m, A=300 mm2 and E=200GPa. Therod in B is aluminum with L=4m, A=500mm2 and E = 70GPa. Determine the verticaldisplacement of the bar at a point where the resultant of the load is acting.