MI8 X 4 Bolts F= 20 kN 60 -75--75- so 250 A rectangular steelbar with 15 mm thickness attached to a 300 mm steel channelusing four tight fitted bolts located at A, B, C, and D. For a F = 20 kN load find: (a) The resultant load on each bolt (Fa, Fa, Fo, Fo=?) (b) The maximum shear stress in each bolt (T=?) (c) The maximum bearing stress occurred on the construction (OMAX=?) Note:All dimensions are given in mm unit.
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- A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?A vertical pole consisting of a circular tube of outer diameter 5 in. and inner diameter 4.5 in. is loaded by a linearly varying distributed force with maximum intensity of q0, Find the maximum shear stress in the pole..17 A mountain-bike rider going uphill applies torque T = Fd(F = l5lb, d = 4 in.) to the end of the handlebars ABCD by pulling on the handlebar extenders DE. Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A). Segments AB and CD are prismatic with lengths L, = 2 in.andL3 = 8.5 in, and with outer diameters and thicknesses d01 = 1.25 in. 101 = 0.125 in. and d03 = O.87in.,i03 = 0.ll5in, respectively as shown. Segment BC’ of length L, = 1.2 in. however. is tapered, and outer diameter and thickness vary linearly between dimensions at B and C. Consider torsion effects only. Assume G = 4000 ksi is constant. Derive an integral expression for the angle of twist of half of the handlebar tube when it is subjected to torque T = Fd acting at the end. Evaluate ‘b1-, for the given numerical1ues.
- A steel bar has a square cross section of width b = 2.0 in. (sec figure). The bar has pinned supports at the ends and is 3.0 ft long. The axial forces acting at the end of the bar have a resultant P = 20 kips located at distance e = 0,75 in, from the center of the cross section. Also, the modulus of elasticity of the steel is 29,000 ksi. Determine the maximum compressive stress max, in the bar. If the allowable stress in the steel is 18,000 psi, what is the maximum permissible length Lmaxof the bar?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.)A vertical pole of aluminum is fixed at the base and pulled at the top by a cable having a tensile force T(see figure). The cable is attached at the outer edge of a stiffened cover plate on top of the pole and makes an angle a = 20° at the point of attachment. The pole has length a = 2.5 m and a hollow circular cross section with an outer diameter d2= 280 mm and inner diameter d1= 220 mm. The circular cover plate has diameter 1.5d2 Determine the allowable tensile force Tallow in the cable if the allowable compressive stress in the aluminum pole is 90 MPa.
- Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.Two pipes {L, = 2.5 m and L, = 1.5 m) are joined al B by flange plales (thickness (, = 14 mm) with five bolts [dlt, = 13 mm] arranged in a circular pal tor n (see figure). Also, each pipe segment is atlaehed to a wall (at .1 and ( '. see figure! using a base plate Uh = 15 mm) and four bolts (dM, = 16 mm). All bolts are tightened until just snug. Assume £, = 110 GPa,E2 = 73 GPa,», = 0.33,andv, = 0.25. Neglect the self-weight of the pipes, and assume the pipes are in a stress-free stale initially. The cross-sectional areas of the pipes are At = 1500 mm: and A2 = (3/5)4. The ollter diameter of Pipe 1 is 60 mm. The outer diameter of Pipe 2 is equal to the inner diameter of Pipe 1. The bolt radius r = 64 mm for both base and flange plates. (a) If torque '/'is applied at .v = Lt. find an expression for reactive torques Iit and IL in terms of T. (b) Find the maximum load variable /'(i.e., Tmal) if allowable torsional stress in the two pipes is Tall0* = 65 MPa-id Draw torsional moment iTMD i and torsional displacement (TDD) diagrams. Label all key ordinales. What is '/>.ll('.' (d) Find mail, if allowable shear and bearing stresses in the base plate and flange bolts cannot be exceeded. Assume allowable stresses in shear an.: :vari:'.g I all bolls are r |Nill, = 45 MPa andtr MaK =90 MPa. (e) Remove torque Tat x — L,. Now assume the flange-plate bolt holes are misaligned by some angle ß (see figure). Find the expressions for reactive torques Rx and R2 if the pipes are twisted to align the flange-plate bolt holes, bolts are then inserted, and the pipes released. (f) What is the maximum permissible misalignment angle ß mix if allowable stresses in shear and bearing for all bolts [from part (d)] are not to be exceeded?A steel column ( E = 30 X 103 ksi) that is fixed at the base and free at the top is constructed of a W8 x 35 wide-flange member (sec figure). The column is 9.0 ft long. The force P acting at the top of the column has an eccentricity e = 1.25 in. If P = 40 kips, what is the maximum compressive stress in the column? If the yield stress is 36 ksi and the required factor of safety with respect to yielding is 2.1, what is the allowable load Pallow?
- Three round, copper alloy bars having the same length L but different shapes are shown, in the figure. The first bar has a diameter d over its entire length, the second has a diameter d over one-fifth of its length, and the third has a diameter d over one-fifteenth of its length. Elsewhere, the second and third bars have a diameter Id. All three bars are subjected to the same axial load P. Use the following numerical data: P = 1400 kN, L = 5m,d= 80 mm, E= 110 GPa. and v = 0.33. (a) Find the change in length of each bar. (b) Find the change in volume of each bar.A flying but tress transmit s a load P = 25 kN, acting at an angle of 60º to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h = 5.0 m and rectangular cross section of thickness t = 1.5 m and width b = 1.0 m (perpendicular to the plane of the figure). The stone used in the construction weighs y = 26 kN/m3. What is the required weight W of the pedestal and statue above the vertical buttress (that is, above section A) to avoid any tensile stresses in the vertical buttress?An elevated jogging track is supported at intervals by a wood beam AB (L = 7.5 ft) that is pinned at A and supported by steel rod BC and a steel washer at B. Both the rod (dBC= 3/16 in.) and the washer (dB= 1.0 in.) were designed using a rod tension force of TBC=415 lb. The rod was sized using a factor of safely of 3 against reaching the ultimate stress tru— 60 ksi. An allowable bearing stress sba= 565 psi was used to size the washer at B. A small platform HF is suspended below a section of the elevated track to support some mechanical and electrical equipment. The equipment load is uniform load q = 50 lb/ft and concentrated load WE= 175 lb at mid-span of beam HF. The plan is to drill a hole through beam ABaX £land install the same rod (dBC) and washer) dB) at both D and F to support beam HF. (a) Use s and to check the proposed design for rod DF and washer d,: are they acceptable? (b) Re-check the normal tensile stress in rod BC and bearing stress at 8 if either is inadequate under the additional load from platform HF. Re-design them to meet the original design criteria.