Stiffness Matrix Method

[xkybb]

Hello!

According to my understanding, Stiffness Matrix Method is often applied for structural analysis (both computer and manual) in obtaining the forces/moments in structural elements.

However, it seems that the Stiffness Matrix Method and the Beam Curvature equation only works when the Material of the element is homogenous and isotopic, while in reality the structural elements are usually non homogenous (eg. a RC beam).

Therefore, let say in designing a RC frame, I wonder why it is OK to directly use the forces/moments obtained from stiffness matrix equation to design the structural elements without verifying the forces/moment by looping the analysis with the revised sectional properties with the provision of reinforcement?

Is that because the movement (eg.strain) of the section under loading will be smaller after the provision of reinforcement, and therefore the resultant forces/moment transfer to the structural elements must be smaller?

 

[angrypom]

Material non-linearity can be incorporated into the stiffness method using Newton-Raphson iterations until convergence is achieved.
Materially nonlinear plastic analysis is permitted in most standards, but in design practice, the complex calculations are rarely justified due to difficulties in material descriptions and the large amount of computer time required.
Additionally, the combination of resulting load cases is no longer possible which increases the work load substantially.
Because of this, design is usually based on linear elastic material behaviour with redistribution of forces. The accuracy of the simplified analysis is generally sufficient.

 

[xkybb]

Reply to angrypom,

Really thx to your explanation and I found it very useful.

Based on my understanding, is that means the inclusion of material non-linearly is only used to achieve a more economical design, and when the designer want to further reduce the resultant forces/moment on the element by iterations?

If that is the case,can I claimed that the simplified linear analysis is more conservative as the member displacement (eg.rotation, strain)and thus stress are higher by ignoring the stiffening effect of the reinforcement?

Sorry for my poor English :[

 

[angrypom]

Generally, yes. Materially non-linear analyses optimise the structure by consideration of load redistributions to exploit additional resistance and a reduction of member forces in the case of restraints which is not considered in linear-elastic analyses.