6. Consider a bar element as shown below with length L, cross sectional area A, and Young'sModulus E. The bar element is subjected to a compressive load P. Nodes 1 and 2experience displacements of u, and u2. Given Hooke's Law, where stress o is given by:Δυo = E ɛ x EAxuse equilibrium requirements to solve for the forces of fi and f2 at the nodes and showhow those equations can be used to derive the stiffness matrix of the bar.U1, fiUz, f2P2

Solution Force at any node given by the following formula fi=AELuiWhere ui=Displacement at any node…

6. Consider a bar element as shown below with length L, cross sectional area A, and Young Modulus E. The bar element is subjected to a compressive load P. Nodes 1 and experience displacements of uj and u2. Given Hooke's Law, where stress o is given by: Δυ o = E ɛ x E Ax use equilibrium requirements to solve for the forces of fi and f2 at the nodes and show how those equations can be used to derive the stiffness matrix of the bar. U1, fi Uz, f2 P 2

6. Consider a bar element as shown below with length L, cross sectional area A, and Young Modulus E. The bar element is subjected to a compressive load P. Nodes 1 and experience displacements of uj and u2. Given Hooke's Law, where stress o is given by: Δυ o = E ɛ x E Ax use equilibrium requirements to solve for the forces of fi and f2 at the nodes and show how those equations can be used to derive the stiffness matrix of the bar. U1, fi Uz, f2 P 2

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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Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.

Question

6. Consider a bar element as shown below with length L, cross sectional area A, and Young's
Modulus E. The bar element is subjected to a compressive load P. Nodes 1 and 2
experience displacements of u, and u2. Given Hooke's Law, where stress o is given by:
Δυ
o = E ɛ x E
Ax
use equilibrium requirements to solve for the forces of fi and f2 at the nodes and show
how those equations can be used to derive the stiffness matrix of the bar.
U1, fi
Uz, f2
P
2

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