What do we do when the moment capacity of a steel section is greater than 1.2p*Z?

Question

In the design of steel beams according to BS 5950: part 1, clause 4.2.5 states that the moment capacity of a section,
M = p*S < 1.2*p*Z
where p - the design strength of steel (in Pascal)
S - plastic modulus of the section (in cubic meters)
Z - elastic modulus of the section (in cubic meters)
What is the implication of this limit on the moment capacity? What should be done if this condition is not satisfied in the design?

Answer 1

the equation should be more than 1.2pZ not less. It is to prevent the onset of plasticity below working load.

Answer 2

I'm not terribly familiar with British codes, but I do believe that this is delving into the realm of plastic design, or maybe the code is setting plastic hinge failure as the "ultimate strength" of the member. I will say that I think that Z is the plastic modulus and S is the elastic modulus.

Plastic design I think was a precursor to what we in the States call LRFD, Load and Resistance Factor Design, which is also based on the plastic modulus. The assumption here is that the ultimate failure of the beam occurs in the plastic region of the stress strain curve due to the formation of a hinge at the point of failure. The plastic limit is somewhat higher than the elastic limits used for Allowable Stress Design.

So I think what they are doing is setting the upper limit of elastic design such that it cannot exceed the limits of plastic design. I don't see how this condition could ever occur, but apparently someone writing the British Standard thinks that the limit is necessary.

Answer 3

Look if the limit vaue greater then you end up sizing a section where the continued deformation will be bound to occur and can lead to crack failure. As an alternate if you use higher section then the overall economics will have an impact as there will be changes in the connected columns.

Answer 4

Use a bigger section or a higher mod. of elastisity if the condition is not met!!!