Consider two axially loaded columns, namely, 1 and 2, made of a linear elastic material with Young's modulus 2 × 10³ MPa, square cross-section with side 10 mm, and length 1 m. For Column 1, one end is fixed and the other end is free. For Column 2, one end is fixed and the other end is pinned. Based on the Euler's theory, the ratio (up to one decimal place) of the buckling load of Column 2 to the buckling load of Column 1 is

Consider two axially loaded columns, namely, 1 and 2, made of a linear elastic material with Young's modulus 2 × 10³ MPa, square cross-section with side 10 mm, and length 1 m. For Column 1, one end is fixed and the other end is free. For Column 2, one end is fixed and the other end is pinned. Based on the Euler's theory, the ratio (up to one decimal place) of the buckling load of Column 2 to the buckling load of Column 1 is

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Mechanics of Deformable Bodies 6 in. in.- 5 in. 4 in. A steel tube with the cross section shown carries a torque T. The tube is 6ft and has a constant wall thickness of 3/8in. (a)Compute the torsional stiffness k=TTO of the tube. (b) If the tube is twisted through 0.5°, determine the shear stress in the wall of the tube. Use G=12x 106psi.
1. An aluminum tube AB of circular cross section has a guided supporter at the base and is pinned at the top to a horizontal beam, which supports a load of Q=200 kN as shown in the accompanying illustration. If the outside diameter of the tube is d=200 mm, determine the required thickness, t, of the tube. Use Euler's buckling theory, and assume a safety factor of N=3. (N.B.: For the aluminum used for the column, use E = 72 GPa.) -1.0 1.0 m B THI 1.0 m- Jº= d = 200 mm 200 KN 2.0 m
The beam has a rectangular cross section and is subjected to the loading shown. Determine the components of stress ox, oy, and Txy at point B. 800 N B 1000 N 15 mm 20 mm 20 mm 15 mm 100 mm 10 mm
A uniform structural tubing column AB with a height of 4 m has a cross section as shown in Figure Q4(b). Given E = 200 GPa, A = 2285 mm2, r = 37.5 mm, and I = 3.33 x 10-6 m4: - 1. Calculate the allowable centric load for the column and the corresponding normal stress using Euler’s Formula by considering the factor of safety of 2.0. 2. Assuming that the allowable load, as in Figure Q4(b)(i), is applied at a point 18.75 mm from the geometric axis of the column as per shown in Figure Q4(b)(ii). Figure Q4(b)(iii) shows the cross section of the column. Identify the horizontal deflection at the top of the column and the maximum normal stress in the column.
A cantilever beam AB with a circular cross section and length L =750 mm supports a load P =800 N acting at the free end (see figure). The beam is made of steel with an allowable bending stress of 120 MPa. a. Determine the required diameter dmm(figure part a) of the beam, considering the effect of the beam's own weight. Repeat part (a) if the beam is hollow with wall thickness t =df$ (figure part b); compare the cross-sectional areas of the two
4. A homogeneous steel shaft (G=83GPa) is loaded as shown in the above Figure. Assuming T = 361 (N-m) torsional stress in member AB. Note: Include sign in your final answer if negative (-), assuming the direction of Torsion (T) at Dis positive Given: AB: Length 1.75m, Diameter = 75mm BC: Length = 1.50m, Diameter = 60mm AB: Length = 1.00m, Diameter = 40mm A LA T/2 determine the maximum B T LA D 1200 Nm
STRENGTH OF MATERIALS (NO LONG EXPLANATION NEEDED) PLEASE WITH FBD! RATE WILL BE GIVEN For the given system below, rods A and B support the rigid bar, pinned at O, as it is subjected to load P = 40 kN. The rods are identical except for their lengths. Find the (a) stress in rod A if its cross-sectional is 300mm2 (b) If rod A elongates by 2mm, how much is the elongation of rod B?
A circular aluminum tube with a length of L = 420 mm is loaded in compression by forces P (see figure). L/3 Strain gage -L=420 mm Ⓡ The hollow segment of length L/3 has outside and inside diameters of 64 mm and 39 mm, respectively. The solid segment of length 2L/3 has a diameter of 64 mm. A strain gage is placed on the outside of the hollow segment of the bar to measure normal strains in the longitudinal direction. (a) If the measured strain in the hollow segment is = 430 x 10-6, what is the strain in the solid part? Hint: The strain in the solid segment is equal to that in the hollow segment multiplied by the ratio of the area of the hollow to that of the solid segment. (Enter the magnitude in a unitless form.) (b) What is the overall shortening of the bar (in mm)? mm (c) If the compressive stress in the bar cannot exceed 54 MPa, what is the maximum permissible value of load P? (Enter the magnitude in kN.) kN
A plastic beam of square cross section 30 mm × 30 mm (see figure) is simply supported with span length L = 419. A point load P = 450 N is placed at the midpoint of the beam. Calculate the maximum bending stress in the plastic. Hint: The maximum bending moment is at the midpoint of the beam.
A beam supports has been shown in the bellow figure. The material is gray cast iron. The value of Using Singularity Function Method, Include the Curve Equation. 500N 900N 70 kN/m 100mm mm A В 100mm 4m 8m 6m RA = | Load Diagram Rc = mm Determine the following: a. Draw shear force diagram and bending moment diagram. b. Determine the maximum bending moment, hence maximum stress in compression andtension. c. Determine the maximum shear stress and maximum transverse shear stress. d. Draw the normal stress distribution and transverse shear stress distribution on the beamcross section at the maximum location of bending moment. e. Write and draw the curve equation and determine the highest deflection.
The beams described in the problems for Section 9.9 have constant flexural rigidity El. A simple beam AB of length L is loaded at the lefthand end by a couple of moment M, (see figure). Determine the angle of rotation 6, at support A. (Obtain the solution by determining the strain energy of the beam and then using Castigliano's theorem.) Mo B L PROB. 9.9-1 Step-by-step solution Step 1 of 5 A Length of the simple beam AB = L Couple of moment at A,= M, Angle of rotation at A= 0,
A uniformly-distributed load w is supported by a structure consisting of rigid bar BDF and three rods. Rods (1) and (2) are 15-mm- diameter stainless steel rods that have an elastic modulus of E = 198 GPa. Rod (3) is a 22-mm-diameter bronze rod that has an elastic modulus of E = 108 GPa. Use a = 1.4 m and L = 2.7 m. For a load magnitude of w = 28 kN/m, calculate (a) the normal stress in each rod. (b) the vertical deflection of the rigid bar at F. 2a (1) |(2) (3) Answers: (a) 01 = i MPa, 02 = i МPа, and og- i MPa (b) VẸ = mm