Axial Deformation on Statically indeterminate beam

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SUMMARY

The discussion focuses on solving axial deformation in a statically indeterminate beam with specific sections and forces. The beam consists of two materials: concrete (E = 25,000 N/mm²) for sections AB and CD, and steel (E = 200,000 N/mm²) for section CD. The forces acting on the beam are 140 kN at point B (left) and 60 kN at point C (right), leading to a net force of 80 kN. The participant is attempting to apply the axial deformation formula PL/AE to determine the compatibility of forces across the sections.

PREREQUISITES
  • Understanding of axial deformation principles in structural engineering
  • Familiarity with Young's modulus (E) for different materials
  • Knowledge of statically indeterminate structures
  • Proficiency in applying the PL/AE formula for deformation calculations
NEXT STEPS
  • Study the method of sections for analyzing statically indeterminate beams
  • Learn about compatibility equations in structural analysis
  • Explore the effects of different materials on axial deformation
  • Review examples of axial deformation calculations in composite beams
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in analyzing and designing statically indeterminate beams will benefit from this discussion.

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Homework Statement



I am trying to find a solution to the below attached image.
The area for AB=CD = 0.8m^2
Area of BC = 0.3m^2

Force at B = 140 kN (left)
Force at C = 60 kN (right)

AB=CD = Concrete with a E of 25,000N/mm^2
CD = Steel with an E = 200,000N/mm^2

Homework Equations



PL/AE

The Attempt at a Solution

This is where I get confused because there is a force acting at B and a force acting at C I am not sure if I need to make a cut at say B or make a cut at C.

I understand the the sum of the forces in X direction have to equal Ax + Dx = 80 kN (As a result of 140 - 60 kN)

Now taking BC as the redundant section

PL/AE for section AB should that of section CD?

I am not sure if I am going about it the right way?

If it was one continuous section with forces only in one direction or even two I understand but because of that section BC it has thrown me out .
 
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Second Attempt at solution

Taking Section AB

δA/D = Fab*L(ab)/AE = Fcd*L(cd)/AE

Now F in AB = 140 kN
and F in CD = -60 kN

*** Edit ***

My compatibility equation of Fab + Fcd = 80 kN?
 
Last edited:

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