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Changes in lengths for axially loaded members under nonuniform conditions

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For a prismatic bar loaded at both ends only, elongation or shortening can be calculated using this equation 𝛿=(P*L)/(AE). in some cases the prismatic bar will not be loaded only at endpoints, the load will be applied at an intermediate point as shown in figure 1. for such case we can calculate the change in length by algebraically summing the elongation or shortening of each segment
Figure 1









 For a prisimatic bar in figure 1-a, the procedure will be as follows:

  • determine the separate segments for the bar, segments AB, BC, CD.
  • Determine the internal axial force at each segment N1, N2, N3 from the free body diagram.
  • For first segment N1 from free body diagram (figure 1-b) N1=PD+PC-PB
  • for second segment N2=PD+PC (figure 1-c)
  • For third segment N3=PD (figure 1-d)
  • then determine the change of length for each segment 𝛿1=(N1*L1)/(A*E), 𝛿2=(N2*L2)/(A*E), 𝛿3=(N3*L3)/(A*E)
  • add 𝛿1, 𝛿2 and 𝛿3 to obtain the total change in length for the bar
Σ𝛿=𝛿1+𝛿2+𝛿3

a similar approach will be followed for a bar consisting of prismatic segments, the internal axial force for each segment should be determined, also the change of length for each segment should be determined 𝛿1=(N1*L1)/(A*E) but the used area should be for the segment under investigation, also the modulus of elasticity(E) for the segment under investigation should be used if different materials used.



Figure 2






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My name is Mohammad Hamdan, and I am a Civil/bridge Engineer with extensive professional background and experience in the field of construction. I have 10+ years of experience in the construction field. During my professional career, my emphasis has been placed on structural projects, mainly bridges, infrastructure and roads. Reading and practicing the design of structures is my passion.i was lucky to be a part of a big team that executed major highway interchanges. I believe in spreading the knowledge, thus, i compose these courses to share my experience and knowledge. My course focuses on the practical side of construction field. On other word, i am sharing some of what new engineers need to know about construction field. Beside working on construction field, i love writing some articles on my website ( curious civil engineer) Moreover, i wrote some engineering papers, you can check them  by searching my name on Google (Mohammad mamon Hamdan)