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- An idealized column is composed of rigid bars ABC and CD joined by an elastic connection with rotational stiffness ßRIat C. There is a roller support at B and an elastic support at D with translationa1 spring stiffness ß and rotational stiffness ßR2. Find the critical buckling loads for each of the two buckling modes of the column. Assume that L = 3 m, ß = 9 kN/m, and ßR]= ßR1= ßL2. Sketch the buckled mode shapes.An idealized column is made up of rigid bars ABC and CD that are joined by a rotational elastic connection at C with stiffness ßR. The column has a roller support at B and a pin support at D. Find an expression for the critical load Pcr of the column.An aluminum pipe column (E = 10,400 ksi) with a length L = 10.0 ft has inside and outside diameters d1= 5.0 in. and d2= 6.0 in., respectively (sec figure). The column is supported only at the ends and may buckle in any direction. Calculate the critical load Pcrfor the following end conditions: (a) pinned-pinned, (b) fixed-free, (c) fixed-pinned, and (d) fixed-fixed.
- Repeat Problem 11.2-14 using L = 12 ft, ß = 0.25 kips/in., ßRl= 1.5ßL2, and ßR2= 2 ßR1.An idealized column consists of rigid bar ABCD with a roller support at B and a roller and spring support at D. The spring constant at D. is ß = 750 N/m. Find the critical load Pcrof the column.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.
- Repeat Problem 2.3-4, but now include the weight of the bar. Sec Table 1.1 in Appendix I for the weight density of steel.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.A long slender column ABC is pinned at ends A and C and compressed by an axial force F (sec figure). At the midpoint B, lateral support is provided to prevent deflection in the plane of the figure. The column is a steel wide-flange section (W 250 × 67) with E = 200 GPa. The distance between lateral supports is L = 5.5 m. Calculate the allowable load P using a factor of safety n = 2.4, taking into account the possibility of Eu 1er buckling about cither principal centroidal axis (i.e., axis 1-1 or axis 2-2).
- The figure shows an idealized structure consisting of two rigid bars with pinned connections and linearly elastic rotational springs. Rotational stiffness is denoted ßR. Determine the critical load Pcrfor the structure.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 aluminum bar has length L = 6 ft and diameter d = 1.375 in. The stress-strain curse for the aluminum is shown in Fig. 1.34. The initial straight, line part of the curve has a slope (modulus of elasticity) of 10.6 × 106 psi. The bar is loaded by tensile forces P = 44.6 k and then unloaded. (a) That is the permanent set of the bar? (b) If the bar is reloaded. what is the proportional limit? hint: Use the concepts illustrated in Figs. l.39b and 1.40.