Q3) A short stepped bar is shown in Figure below. The stiffness of the large section is 12 kN/mm and the stiffness of the small section is 8 kN/mm. End 1 is fixed and an axial load of 6 kN acts at node 3. Determine the displacements at node 2 and node 3. 12 kN/mm 6 kN Figure (1)
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- A column, pinned at top and bottom, is made up of two C 6 x 13 steel shapes (see figure) that act together. Find the buckling load (kips) if the gap is zero. Find required separation distance d(inches) so that the buckling load is the same in y and z directions. Assume that E = 30,000 ksi and L = 18 ft. Note that distance d is measured between the centroids of the two C shapes.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 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 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.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.Slender column ABC is supported at A and C and is subjected to axial load P. Lateral support is provided at mid-height if but only in the plane of the figure; lateral support perpendicular to the plane of the figure is provided only at ends A and C. The column is a steel W shape with modulus of elasticity E = 200 GPa and proportional limit pl= 400 MPa. The total length of the column L = 9 m. If the al low-able load is 150 kN and the factor of safety is 2.5, determine the lightest W 200 section that can be used for the column. (See Table F-l(b), Appendix F).
- The hoisting arrangement for lifting a large pipe is shown in the figure. The spreader is a steel tubular section with outer diameter 70 mm and inner diameter 57 mm. Its length is 2.6 m, and its modulus of elasticity is 200 GPa. Based upon a factor of safety of 2.25 with respect to Euler buckling of the spreader, what is the maximum weight of pipe that can be lifted? (Assume pinned conditions at the ends of the spreader.)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.Three pinned-end columns of the same material have the same length and the same cross-sectional area (see figure). The columns are free to buckle in any direction. The columns have cross sections as: (a) a circle, (b) a square, and (e) an equilateral triangle. Determine the ratios Pa: Pb: Pcof the critical loads for these columns.
- An idealized column is made up of rigid segments ABC and CD that are joined by an elastic connection at C with rotational stiffness ßR= 100 kip-in./rad. The column has a roller support at B and a sliding support at D. Calculate the critical load Pcrof the column.The figure shows an idealized structure consisting of two rigid bars joined by an elastic connection with rotational stiffness ßR. Determine the critical load PCTfor the structure.An idealized column is composed of rigid bars ABC and CD joined by an elastic connection with rotational stiffness ßRat C. There is an elastic support at B with translational spring stiffness ß and a pin support at D. Find the critical buckling loads for each of the two buckling modes of the column in terms of ßL. Assume that ßR= ßL2. Sketch the buckled mode shapes.