For more further information on this topic, please see the laboratory handout titled "Flexibility and Stiffness of a Portal Frame".

- The structure for this experiment is a simply supported portal frame, shown in the figure below.

- The force-displacement relationship for three points of the frame (center of the top, center of the roller supported column, and base of the roller supported column) need to be determined.

- The relationship to be constructed experimentally is:

here

P_{1}, P_{2}, P_{3}andD_{1}, D_{2}, D_{3}are the forces and displacements of points 1, 2, and 3, respectively.

- Matrix [
*f*] is the flexibility matrix.

- The flexibility matrix can be constructed by the unit load method.

If:

P_{1}= 1.0

P_{2}=P_{3}= 0.0Then:

f_{11}=D_{1}

f_{21}=D_{2}

f_{31}=D_{3}

- This procedure is repeated for:

P_{2}= 1.0

P_{1}=P_{3}= 0.0and:

P_{3}= 1.0

P_{1}=P_{2}= 0.0These results can be used to construct the second and third columns of the flexibility matrix.

- The stiffness matrix of the structure, [
*K*], is now defined as the inverse of [*f*], such that:

where: