Strong column weak beam and P-M interaction
These are the two checks that most often decide the size of a reinforced-concrete column in a moment frame. This page describes how sazeh does each of them.
Strong column, weak beam
The check keeps the columns of a joint stronger than the beams that frame into it, so that hinges form in the beams first. It is made at every joint and in each direction.
| Item | How it is taken |
|---|---|
| Requirement | The sum of the column flexural strengths at the joint is at least 1.2 times the sum of the beam flexural strengths |
| Strengths used | Nominal strengths, not design strengths |
| Output | The ratio at every joint, and the count of joints that fail |
The nominal strength is used on both sides. A column reduction factor of 0.65 and a beam factor of 0.9 are different, so using design strengths on both sides would shrink the ratio by about 28% and reject a sound joint.
The sheet counts joints, not rows. A joint that fails under several combinations is one failed joint, and 318 failing rows can be only 34 columns.
P-M interaction of a column
The interaction curve gives the pairs of axial load P and moment M that a section can carry. The demand of every combination is plotted against the design curve, and the ratio is the distance to it.
- How the curve is built. A strain-compatibility sweep over the equivalent rectangular stress block, with the bars idealised as discrete steel layers. The curve is for one axis at a time, and the section is taken as unconfined.
- Bars on four faces. The bars are placed on all four faces. Putting half of them on each of two end faces would give the largest possible lever arm to all of them and overstate the moment strength by up to 19% at high axial load, which is exactly the case of a gravity column.
- Both limits of the axial force. The check uses the largest compression and the least compression (or tension) of the envelope, because uplift can govern a column beside a wall.
- Slenderness. The moment is amplified for the second-order effect of the member. A 400 mm square column over a 3.2 m storey has a slenderness of about 27, which is above the limit of 22 below which the effect may be ignored, so the amplification is active in most ordinary frames. On one test grid it ranged from 1.012 to 1.187.
Where the check is made
The ratio is computed from the nominal flexural strengths of the members framing into each joint, taken from the model that you upload. sazeh reads ETABS files only: the strong column, weak beam check of a STAAD model cannot be made here.
Biaxial bending
Every column of a building carries moment about both axes at the same time, and both use the same concrete. A row that looks at the two axes separately passes columns that fail together. On one test grid the worst uniaxial row was 0.358 and the worst biaxial row was 0.564.
The biaxial row combines the two uniaxial curves. Above an axial load of 0.1 times the gross area times the concrete strength it uses the Bresler reciprocal-load method, and below that load it uses a load-contour curve, because the reciprocal method misbehaves at low axial load.
Steel box columns
A steel box column is checked for compression and for the interaction of axial force with bending about both axes. Checking compression alone would pass a column under gravity load while the frame moment is ignored: on a five-storey steel frame the worst compression ratio was 0.390 and the worst interaction ratio was 0.796.
Related pages
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