Given: The uniaxial bar shown below is homogeneous, prismatic and has a distributed axial loadof p,(x)= px, where p=constant (note: P, is not a constant!) applied along its length asshown.E=constantLeft end is fixed (u(x=0)%3D0)→ → - → →A=constantRequired: 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) (fora 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

1) Using uniaxial theory we try to derrive the espressions given

Required: 1) Using uniaxial bar theory, derive an expression for each of the following: ) P= P(x, p?) -) o = 0,(x, p, A,L,E) ) E, = €„ (x, p?, 4,L, E) ) u = u(x, p,A,L,E) ) Plot the results of a)-d) on four different graphs: P=P(x), Ox=0x(x), Ex=Ex(x), and u=u(x) (for given value of the input loads, geometry, and material properties) ) Determine the reactions at each end, P(x=0) and P(x=L) ) Determine the maximum axial deflection umax and determine its coordinate location

Required: 1) Using uniaxial bar theory, derive an expression for each of the following: ) P= P(x, p?) -) o = 0,(x, p, A,L,E) ) E, = €„ (x, p?, 4,L, E) ) u = u(x, p,A,L,E) ) Plot the results of a)-d) on four different graphs: P=P(x), Ox=0x(x), Ex=Ex(x), and u=u(x) (for given value of the input loads, geometry, and material properties) ) Determine the reactions at each end, P(x=0) and P(x=L) ) Determine the maximum axial deflection umax and determine its coordinate location

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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Question

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

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