Analysis of Knee-Braced Portal Frames for Vertical Loading: Part 1

Knee-braced portal frames such as those shown in Figs. 1 and 2 are encountered from time to time in the design of buildings. The analysis of these bents for the vertical loading is easily done if a computer and necessary software are accessible to form and solve the stiffness matrix for the frame. If they are not accessible, then one is in a quandary, because the simultaneous deflections in the beam and the columns have to be accounted for in the solution. This paper looks into the longhand solution of such portal frames. Equations are developed and solutions given which are easy to apply. What is needed are the unit load and beam load deflections at the knee-brace locations. And, for given frame dimensions, these are calculated only once. As the member sizes are altered, one need only to change the matrix coefficients, which can be accomplished in little time. With two or three trials, economical selection of the members can be made.