Last Updated on September 21, 2026 by Maged kamel
Analysis of a portal frame with fixed supports at the base.
The Portal frame is analyzed into one frame and two cantilevers.
The second case is a portal Frame with fixed supports at the base; the inflection points are located at mid-height of the columns, in addition to the hinge at the Midpoint of the girder. This solution is an approximate solution to facilitate the Design.
The upper part above the hinge is represented separately, with three hinges. This part is the same as the one we have already solved: a portal frame hinged at the supports. The only difference is that the height is h/2.
The joint forces derived earlier were P*h/L at the left and right supports, with the same magnitude but opposite directions.
At the left joint, P*h/L acts downwards, while at the right support, it acts upwards, so the joint Reaction = P*h/L.
Estimation of the portal frame reactions.
The height from the upper floor to the lower hinge is equal to h/2.
To estimate the left joint Reaction, it is Reaction*h/(2*L) acting downwards, and at the right support, Reaction = P*Reaction acting upwards due to joint balance. A P*h/(2*L) force acts downwards at the hinge in the left column at height = h/2.
How do you draw a Moment diagram for a portal frame with fixed supports at the base?
We have a horizontal force = P/2 acting to the right and a vertical force = P*h/L acting upwards. Regarding the bending Moment, the Moment due to a couple will rotate in this manner. Then, the support Moment to create stability will act in this direction, anti-clockwise. The Moment will be (P/2)*(h/2)=P*h/4.
Let us have a look at the right portion of the joint. We have P/2 at the right hinge acting from right to left, rather than P/2 from left to right. We have a vertical force, Ph/2L, acting upwards, and an equal and opposite force, Ph/2L, acting downwards.
The couple at the right side =(P/2*h/2), opposed by the Moment at the support.
The Moment at the left support, Ph/4, acts anti-clockwise and equals the Moment at the right support of the portal frame, with fixed supports at the base.
For the Moment values due to superposition, we have a negative Moment, zero at the mid-column height, then reversed at joint C. The slope is 0, then starts to increase as the Moment increases. Let us examine the bending Moment diagram and the other forces at joints. However, the Moment is drawn differently than what we have drawn.
The Moment Value is P*h/4, and the reaction is P*Reaction, a vertical reaction, which we have evaluated. When drawing the Moment, we place it at the tail of the arrow, Yielding the same values.
I have included a practice problem applying this to a portal frame with a fixed base.
Introduction to the m Value for the alignment chart for the unbraced frame.
The new subject is the modified factor m Value. From this UMass Link, I copied valuable information on structural steel Design, including these shapes. I have included a Link to the AISC code teaching aids. Please download the data and check the compression members
. Apply a modification to the alignment chart for the three cases shown in the next slide image.
We will continue our discussion about m values for the side-sway uninhibited in the next Post.
The PDF for this Post and the previous Post is available for viewing and download in the document below.
This is the next Post, 19, a modification to the alignment chart.
For a good Beginner’s Guide to the Steel Construction Manual, 14th ed. Chapter 7 – Concentrically Loaded Compression Members.
For a good A Beginner’s Guide to the Steel Construction Manual, 15th ed. Chapter 7 – Concentrically Loaded Compression Members.
For a good A Beginner’s Guide to the Steel Construction Manual, 16th ed. Chapter 7 – Concentrically Loaded Compression Members.
The Core Teaching Aids for Structural Steel Design Courses include full data, which you can download from the AISC Link. Check the folder for compression members.