To calculate the maximum axial loads for a column based on yielding and buckling about both axes, and allowing for factors of safety. The critical load P for buckling of a column depends on the vertical distance between supports and how the column is connected to those supports. The length L in the T'EI formula Per =- is the distance between points of zero moment. For a pin- L2 supported column, this is the full height of the column. For a column that is not pinned at both ends, the points of zero moment are not at the supports. The equation for the critical load can be modified to use an effective length Le = KL, where K depends on the support conditions. For a column fixed at both ends, K = 0.5. For a column fixed at one end and pinned at the other, K = 0.7 (Figure 1). The equation for the critical load then becomes ’EI Pa (KL)²

To calculate the maximum axial loads for a column based on yielding and buckling about both axes, and allowing for factors of safety. The critical load P for buckling of a column depends on the vertical distance between supports and how the column is connected to those supports. The length L in the T'EI formula Per =- is the distance between points of zero moment. For a pin- L2 supported column, this is the full height of the column. For a column that is not pinned at both ends, the points of zero moment are not at the supports. The equation for the critical load can be modified to use an effective length Le = KL, where K depends on the support conditions. For a column fixed at both ends, K = 0.5. For a column fixed at one end and pinned at the other, K = 0.7 (Figure 1). The equation for the critical load then becomes ’EI Pa (KL)²

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter11: Columns

Section: Chapter Questions

Problem 11.3.18P: A long slender column ABC is pinned at ends A and C and compressed by an axial force F (sec figure)....

See similar textbooks

Similar questions

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 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.
A 10-ft rigid bar AB is supported with a vertical translational spring at A and a pin at B. The bar is subjected to a linearly varying distributed load with maximum intensity q0. Calculate the vertical deform at ion of the spring if the spring constant is 4 kips/in.
A lifeboat hangs from two ship's davits. as shown in the figure. A pin of diameter d = 0.80 in. passes through each davit and supports two pulleys. are on each side of the davit. Cables attached to the lifeboat pass over the pulleys and wind around winches that raise and lower the lifeboat. The lower parts of the cables are vertical and the upper parts make an angle a =15° with the horizontal. The allowable tensile force in each cable is 1800 lb, and the allowable shear stress in the pins is 4000 psi. If the lifeboat weighs 1500 lb, what is the maximum weight that can be carried in the lifeboat?
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.
Two steel wines support a moveable overhead camera weighing W = 28 lb (see figure part a) used For close-up to viewing of field action at sporting, events. At some instant, wire I is at an angle a = 22° to the horizontal and wire 2 is at angle fi = 40°. Wires I and 2 have diameters of 30and 35 mils, respectively. (Wire diameters are often expressed in mils; one mil equals 0.001 in.) (a) Determine the tensile stresses s and s2 in the two wires. (b) If the stresses in wires 1 and 2 must be the same, what is the required diameter of wire 1 ? (c) To stabilize the camera for windy outdoor conditions, a third wire is added (see figure part b). Assume the three wires meet at a common point coordinates (0, 0. 0) above the camera at the instant shown in figure part b. Wire I is attached to a support at coordinates (75 ft, 48 ft, 70 Ft). Wire 2 is supported at (-70 ft. 55 ft, 80 Ft). Wire 3 is supported at (-10 ft. -85 Ft, 75 ft). Assume that all three wires have a diameter of 30 mils. Find the tensile stresses in all three wires
A fixed-end column with circular cross section is acted on by compressive axial load P. The IS-ft-long-column has an outer diameter of 5 in., a thickness of 0.5 in., and is made of aluminum with a modulus of elasticity of 10,000 ksi. Find the buckling load of the column.
A long re Lai nine: wall is braced by wood shores set at an angle of 30° and supported by concrete thrust blocks, as shown in the first part of the figure. The shores are evenly spaced at 3 m apart. For analysis purposes, the wall and shores are idealized as shown in the second part of the figure. Note that the base of the wall and both ends of the shores are assumed to be pinned. The pressure of the soil against the wall is assumed to be triangularly distributed, and the resultant force acting on a 3-meter length of the walls is F = 190 kN. If each shore has a 150 mm X 150 mm square cross section, what is the compressive stress
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.
Repeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.
A suspender on a suspension bridge consist of a cable that passes over the main cable (see figure) and supports the bridge deck, which is Far below. The suspender is held in position by a metal tie that is prevented from sliding downward by clamps around the suspender cable. Let P represent the load in each part of the suspender cable, and let represent the angle of the suspender cable just above the tie. represent the allowable tensile stress in the metal tie. (a) Obtain a formula for the minimum required cross-sectional area of the lie. (b) Calculate the minimum area if P = 130 kN, = 75°, and allow=80 .
Repeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.