3. Deflection of beam-columns Example 1: A simply supported beam-column of length L is subjected to a concentrated load Q at midspan and an axial compressive force P as shown in the figure below. Derive and solve the differential equation of the deflection curve. Then find the max. deflection and max. bending moment. (Neglect self weight) 66

3. Deflection of beam-columns Example 1: A simply supported beam-column of length L is subjected to a concentrated load Q at midspan and an axial compressive force P as shown in the figure below. Derive and solve the differential equation of the deflection curve. Then find the max. deflection and max. bending moment. (Neglect self weight) 66

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

For the beam and loading shown, use discontinuity functions to compute (a) the slope of the beam at B and (b) the deflection of the beam at. A. Assume a constant value of EI = 113000 kip-ft² for the beam; wo = 2.0 kips/ft, LAB = 15 ft. LBC= 8 ft. - Wo A Answer: (a) 8B = (b) VA= LAB rad in. B LBC C X
Consider the frame shown in figure. Suppose that P1 = 5.5 k and P2 = 11 k. Each column has the cross-sectional area indicated. Solve the problem using the cantilever method of analysis. Assume that the internal moment, shear, and normal force in the vertical beam are positive if they act as shown. a) Determine (approximately) the normal force at A. NA = _____ k Submitted Answers ANSWER 1: Deduction: -3% NA = 4.973 k ANSWER 2: Deduction: -3% NA = 3.8254 k ANSWER 3: Deduction: -3% NA = 5.933 k
Consider: a beam made of isotropic material, and itscross-section area is A throughout the entire beam.The beam has a Young’s modulus E. The beam isattached to a roller support (the length/size of thissupport is negligible) at x=0.Calculate the total elongation when the beam issubjected to a leftward concentrated force F atx=3L and a rightward force 3F at x=5L.
A beam is shown in the figure below, and the flexural stiffness of the beam section is constant EI:(a) Use the Moment-area Method to find the Slope after point A is deformed.(b) Same as above, try to find the slope of point B after deformation.(c) Same as above, try to find the vertical deflection of point C (Deflection).
Given: The beam below is welded to the wall at the left end. The beam is of length L. There is a distributed load across the length of the beam. Wo Find a. Identify the boundary conditions you would use to solve for the deflection curve y(x). Note: you do not need to solve for y(x). b. Sketch the deflection you expect the beam to exhibit under this load.
2. Solve the following problem of bars in axial load using the finite element method, finding a) displacements at the nodes, b) reactions at supports, c) forces and stresses in each element. Consider E1=E2=E3=200GPa, A1= 20x10-4 m2, A2= 10x10-4 m2, A3= 8x10-4 m2 for the bars. F2= 40kN, F3= 50kN
This is statics of rigid bodies fundamental concept. Show a step by step solutions.
The structure shown in Figure is subjected by a force P =253 N at central point. Determine the absolute vertical reaction force at A. Solve the problem by assigning 100 beam elements along the path AB. Consider, elastic modulus E = 200 GPa, poisson's ratio v = 0.3, radius R = 500 mm. The ring has a circular cross sectional area with diameter of 10 mm. (The answer unit should be in N). Acceptable error: 4% 1A Yanıt:
Solve the problem by the moment-area method. The beam has constant flexural rigidity EI. A simple beam AB supports two concentrated loads P at the positions shown in the figure. B C 4. 4 A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d = 12 mm, L = 5.4 m, E = 200 GPa, and I = 193 x 10° mm, calculate the magnitude of the loads P (in kN) so that the beam just touches the support at C. 163.87 x kN
Problem: For the beam and loading shown, determine (a) the equation of the elastic curve, and (b) the deflection midway between the supports. Assume that EI is constant for the beam. You can use any method for the beam deflection computation. w(x) = w,x/L³ Wo %3D A B
A simply supported beam is subject to a downwards uniform distributed load, w, as shown below. B A uniform distributed load, w L1 L2 The cross-section of the beam is constant with second moment of area I = 3750 mm², and Young's elastic modulus is E = 200 GPa. The distributed load has magnitude w = 220 N/m. If Point B is distance L₁ (Point C), calculate: the downwards vertical deflection at Point B: C C 435 mm from the left end (Point A) and distance L2 = 385 mm from the right end Round your answer to 3 significant figures. X [Units: mm]
Solve the problem by the moment-area method. The beam has constant flexural rigidity EI. A simple beam AB supports two concentrated loads P at the positions shown in the figure. P d B C 800 L 4 4 4 4 Ⓡ A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d = 12 mm, L = 5.4 m, E = 200 GPa, and I = 193 x 106 mm4, calculate the magnitude of the loads P (in kN) so that the beam just touches the support at C. KN L