Structural analysis stiffness method

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SUMMARY

The discussion focuses on solving a structural analysis problem using the stiffness method, specifically addressing the calculation of forces in a system with one degree of freedom (DOF). The user established the stiffness matrix component K11 as K11 = 2EA/L, incorporating adjustments for member lengths and angles. The final equations derived include P = EAe√3/2L and D = √3e/4, which are critical for determining the forces in the structure. The user successfully navigated the complexities of the problem by manipulating the roller position and applying the stiffness method effectively.

PREREQUISITES
  • Understanding of structural analysis principles
  • Familiarity with the stiffness method in structural engineering
  • Knowledge of matrix equations in engineering mechanics
  • Proficiency in trigonometric functions and their applications in structural calculations
NEXT STEPS
  • Study the application of the stiffness method in multi-degree of freedom systems
  • Explore advanced matrix analysis techniques for structural engineering
  • Learn about the effects of varying member lengths and angles on structural stability
  • Investigate the use of software tools for structural analysis, such as SAP2000 or ANSYS
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in analyzing and designing structures using the stiffness method will benefit from this discussion.

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I need to solve this problem but with member 2 as L+e instead of L, and omit the load..

Since I only see one degree of freedom, i don't know how to set up the matrix to solve for the 3 forces.

I have K11 = EA/L + (EA/(L+e))cos2(30) + EA/L cos2(60) but since there is only 1 DOF and no loads, i don't have much to make a matrix equation with..

I tried moving the roller to the right ecos(30) and trying to solve for the forces like that, but couldn't get much.. any ideas?
 
Last edited:
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I figured it out..

AD = Adm + kD

AD = 0

K11 = EA/L + (EA/(L+e))cos2(30) + EA/L cos2(60) = 2EA/L

Adm = PL/EA = ecos(30) --> P = EAe√3/2L

--> D = √3e/4

AR1 = Arm + FrD

AR1 = EA√3e/4L
AR2 = -5EAe/8L
AR3 = EA√3e/8L
 
Last edited:

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