Displacement d.o.f. d; at ends of a uniform bar element have the directionsshown. Write an expression for II, in terms of these d.o.f. From the sta-tionary condition dII, = 0, obtain the element stiffness matrix that operateson these four d.o.f.d4A,EProblem 3.7

Derivation of the element stiffness matrix for a bar element using the principle of minimum…

Answered: Displacement d.o.f. d; at ends of a…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Given: The uniaxial bar shown below is homogeneous, prismatic and has a distributed axial load of p,(x)= px, where p=constant (note: P, is not a constant!) applied along its length as shown. E=constant Left end is fixed (u(x=0)%3D0) → → - → → A=constant Required: 1) Using uniaxial bar theory, derive an expression for each of the following: a) P= P(x, p;) b) o, 3D о, (х, р,, А, L, E) c) E = E (x, p, 4,L, E) d) и %3D и(х, р%, 4, L, E) 2) Plot the results of a)-d) on four different graphs: P=P(x), Om=0xx(x), Ex=Ex(x), and u=u(x) (for a given value of the input loads, geometry, and material properties) 3) Determine the reactions at each end, P(x=0) and P(x=L) 4) Determine the maximum axial deflection umax and determine its coordinate location
PLEASE SHOW COMPLETE AND STEP BY STEP SOLUTION
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).
Figure below shows a uniformly tapering bar of rectangular cross-section of length L and thickness t. The width of the bar at one end is b₁ and the width at the other end is b2, where (b₂> b₁). The bar is subjected to an axial force P. The axial deformation due to load P is given by _mm. b₂ PL atE b₁ = 20 mm b₂-40 mm -In () then the value of (a + c) is
8 Expansion is an axial deformation. 9 True 10 False The coordinates of centroid locate the ge ometric center of the cross-section of the material.( True False Torsional stress is also known as bending stress.( True False
Part F
Problem 3: For the plane truss structure shown in figure below, determine the displacement of node 1 using the stiffness method. Also determine the stress in all elements. Let: A = 10 in², E = 106 psi, and L = 150 in L 4 3 25° 25° 2 300 lb 45°

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Displacement d.o.f. d; at ends of a uniform bar element have the directions shown. Write an expression for II, in terms of these d.o.f. From the sta- tionary condition dI, = 0, obtain the element stiffness matrix that operates on these four d.o.f. %3D A,E d1 Problem 3.7