330k 198k 132k N 16 in.- 12 in. 12 in. E = 29×10086 D = 1.07 in (bigger rod) D=107mind(570.618 in. rod) Determine the deformation of the steel rod shown under the given loads. SOLUTION: • Divide the rod into components at the load application points. • Apply a free-body analysis on each component to determine the internal force • Evaluate the total of the component deflections.
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- A pinned-end strut of aluminum (E = 10,400 ksi) with a length L = 6 ft is constructed of circular tubing with an outside diameter d = 1 in. (sec figure). The strut must resist an axial load F = 4 kips with a factor of safety n = 2.0 with respect to the critical load. Determine the required thickness t of the tube.Repeat Problem 11.2-14 using L = 12 ft, ß = 0.25 kips/in., ßRl= 1.5ßL2, and ßR2= 2 ßR1.A cantilever aluminum column has a square tube cross section with an outer dimension of 150 mm. The column has a length L = 4 m and is designed to support an axial load of 45 kN. Find the minimum required thickness of the section if the factor of safety n = 2.5 with respect to buckling. Assume that the modulus of elasticity is 72 GPa and the proportional limit is 480 MPa.
- 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.A steel pad supporting heavy machinery rests on Four short, hollow, cast iron piers (see figure). The ultimate strength of the cast iron in compression in 50 ksi. The outer diameter of the piers is d = 4.5 in, and the wall thickness is t = 0.40 in. Using a factor of safety of 3.5 with respect to the ultimate strength, determine the total load P that can be supported by the pad.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.
- 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.A mountain bike rider going uphill applies a force P = 65 N to each end of the handlebars AB CD, made of aluminum alloy 7075-T6, by pulling on the handlebar extenders (DF on right handlebar segment). 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 Lvand L3 and with outer diameters and thicknesses J01, /01 and d03, /03, respectively, as shown. Segment BC of length L2, however, is tapered, and outer diameter and thickness vary linearly between dimensions at B and C Consider shear, torsion, and bending effects only for segment AD; assume DFis rigid. Find the maximum tensile, compressive, and shear stresses adjacent to support A. Show where each maximum stress value occursA rigid bar of length L is supported by a linear elastic rotational spring with rotational stiffness ßRat A. Determine the critical load Pcr for the structure.
- A steel column (E = 30 x 103 ksi) with pinned ends is constructed of a W10 x 60 wide-flange shape (sec figure). The column is 24 ft long. The resultant of the axial loads acting on the column is a force P acting with an eccentricity n = 2.0 in. If P = 120 kips, determine the maximum compressive stress ff^ in the column. Determine the allowable load Pallowif the yield stress is ( y =42 ksi and the factor of safety with respect to yielding of the material is n = 2.5.A fixed-pinned column is a W310 × 21 steel shape and is designed to carry an axial load of 125 kN. Determine the maximum permissible height L of the column if a factor of safety n = 2.5 is required with respect to the buckling of the column. Use E = 205 GPa and assume that the proportional limit is 340 MPa. The column may buckle about either axis of the cross section.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.