Engineering Total Lateral Stiffness from Stiffness Matrix

Thread starter Tygra
Start date Feb 7, 2025
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Frame Moment

AI Thread Summary

To compute the total static stiffness of a Moment Resisting Frame, the stiffness matrix has been established using the direct stiffness method, but further steps are needed to derive the total stiffness. The stiffness matrix provided includes terms based on the modulus of elasticity, second moment of area, frame width, and height. The user is referencing a book, "Dynamics of Structures," for guidance but is struggling with the application of the concepts. Assistance is requested to clarify the process for calculating total stiffness from the stiffness matrix. Understanding these calculations is crucial for accurate structural analysis and design.

Feb 7, 2025

Tygra

Homework Statement: How to use a stiffness method matrix to find total stiffness

Relevant Equations: See in post

Hi all,

I am working on the following Moment Resisting Frame:

The frame has the following structural properties:

Matlab:

E = 2.1E+08   % Modulus of elasticity;
I = 0.000117  % Second moment of area
L = 5;   % Frame width
h = 3;  % Frame height

I want to compute the total static stiffness of the frame. I have calculated the stiffness matrix for this frame using the direct stiffness method, but that does not give you the total stiffness.

Here is the stiffness matrix K

Matlab:

K =    [24*E*I/h^3 6*E*I/h^2 6*E*I/h^2;
       6*E*I/h^2 (4*E*I/h + 4*E*I/L) 2*E*I/L;
       6*E*I/h^2 2*E*I/L (4*E*I/h + 4*E*I/L)]

I am following this book (Dynamics of Structures) that shows you how to do it, but I don't quite get it.

Could someone help me please?

Many thanks,

Tygra

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