Lateral restraining systems 2

[sdz]

AS3990 has requirements for strength and stiffness of lateral restraints;
3.3.4.3 Stiffness A single lateral restraint shall be designed in such a way that the transverse deflection of the critical flange or chord at the point being restrained shall not exceed 0.0025L, where L is the span of the restrained member (Clause 5.8), when subjected to the force of 0.025P defined in Clause 3.3.4.2.

AS4100 has requirements for strength only;
6.6.2 Restraining members and connections At each restrained cross-section of a compression
member, the restraining members and their connections which are required to brace the compression
member shall be designed for the greater of—
(a) the restraining member forces specified in Clause 6.6.1; and
(b) 0.025 times the maximum axial compression force in the member at the position of the
restraint, ...

What has happened to stiffness requirements?
Can we safely forget about them?

 

[asixth]

Good question,

It is something that I have struggled to understand. I always thought that the restraint requirements should include both a force and deflection criteria. I made note of this in a concurrent thread in the Struct Eng Other Topics forum.

thread507-268880

I have the same question for flange lateral restraint in flexural members where reference is made to 2.5% of the flange force. I think it should also include a stiffness requirement. I will look through my Kitipornchai book tomorrow to see if I can find anything on a stiffness requirement.

 

[jhardy1]

Clause C6.6.2 of the Commentary to AS 4100 states:

The restraint is required to be able to transfer 2.5% of the axial compression force in the member being restrained, where this is greater than the force specified in Clause 6.6.1. A stiffness requirement is not given even though there is a theoretical solution (Ref. 27). This follows the finding (Ref. 28) that the requirements for centrally braced columns are satisfied by practical braces which satisfy the 2.5% rule.

The two references are:

27 Mutton, B.R., and Trahair, N.S., ‘Stiffness Requirements for Lateral Bracing’, Journal of the Structural Division, ASCE, Vol. 99, No. ST10, Oct 1973, pp. 2167-2182.
28 Mutton, B.R., and Trahair, N.S., ‘Design Requirements for Column Braces’, Civil Engineering Transactions, Institution of Engineers, Australia, Vol. CE17, No. 1, 1975, pp 30-36.

Nevertheless, I have always found it odd that the stiffness requirement has been omitted, as the fundamental requirement to prevent lateral buckling is in fact a stiffness requirement, rather than a force requirement.

You can demonstrate this yourself quite easily if you have access to software which can undertake linear buckling analysis – e.g. Space Gass, Microstran, Strand7, etc. Set up a model of a classic Euler column, with a lateral spring providing restraint at mid-height. We want to investigate the increase in buckling load of the column as the stiffness of the spring increases. For an unbraced column (ks = 0.0 N/m), the buckling load will be the Euler Load for the full column length: P1 = pi^2*E*Ixx/L^2. For a fully restrained column (ks = infinity), the buckling load will be the Euler Load for a column with half the effective length: P2 = pi^2*E*Ixx/(L/2)^2 = 4 * P1.

Consider the case where we are trying to design a spring restraint to fully restrain the mid-point of the column, using a spring with stiffness given by the old stiffness provisions. We would be designing a restraint which can take a lateral load of P2/40 (remember, the fully braced column should be designed for the Euler Load of the reduced effective length), and we would want the deflection under this load to be no greater than L/400. This gives a minimum stiffness requirement of kcrit = (P2/40)/(L/400) = 40*pi^2*E*Ixx/L^3.

Using your buckling program, evaluate the buckling load as k varies from significantly less than kcrit to significantly greater than kcrit. You should find that for k ~ 1% kcrit, the buckling load is barely greater than P1; that is, springs with a stiffness of less than ~ 1% kcrit have no significant restraining effect. At 10% kcrit, the buckling load will increase to approximately 2 * P1; that is, springs with stiffness ~ 10% kcrit have a significant effect on the buckling load, but do not FULLY restrain the member. Once the stiffness rises to ~ 70% kcrit, the buckling load is approximately equal to P2 = 4 * P1, and any further increase in spring stiffness has no further increase on the buckling load.

That is, lateral restraints with stiffness given by the (P/40)/(L/400) rule will fully restrain the braced member. Lateral restraints which can carry the P/40 load, but which do not meet the L/400 deflection criterion, may only partially restrain the member.

 

[asixth]

jhardy1

good post

 

[apsix]

I'm not disagreeing with what you wrote jhardy1 (Julian?), but you would hope that there is a good reason why AS4100 and now also EC3 have not used stiffness as one of the criteria.

Has anyone seen the two references by Mutton and Trahair?

 

[jhardy1]

No, I don't have access to the two references from the Commentary. I do however have a copy of "The Behaviour & Design of Steel Structures" by Trahair & Bradford (2nd edition, 1988), which was revised to coincide with the first draft release of AS 4100.

Section 3.5.2 of Trahair & Bradford discusses the theoretical stiffness requirements for intermediate restraints, and then states:

"There are no restraint stiffness limitations in the AS, but instead restraints are generally required to be able to transmit 2.5% of the force in the member restrained. This follows a finding [Mutton & Trahair] that most practical restraints which satisfy this requirement are sufficiently stiff."

I would agree that _MOST_ practical members which can carry 2.5% of the axial force of the restrained member would have sufficient stiffness to meet the theoretical requirement, but there are certainly examples of restraining members which do not.

For example, it is quite common to use a horizontal channel member in a toes-down orientation to act as the horizontal restraining member in a K-braced or X-braced support trestle. I have seen many cases where the channel can easily carry 2.5% of the design bracing force as an ultimate horizontal load applied where the braces connect, but the resulting out of plane deflection would exceed L/400 for the supported members. I wonder whether the ultimate load carrying capacity of such a structure is as high as expected?

Personally, I still always use the P/40 / L/400 rule when designing intermediate restraints, even though AS 4100 has relaxed this requirement.

 

[sdz]

apsix,

I got a copy of 2nd reference from IEA library as scanned pdf. Do you want a copy?

 

[asixth]

yes please

 

[sdz]

Here it is. I should have uploaded it in the first place.

 

[jhardy1]

sdz,

Thanks for posting!

I found it fascinating that the Conclusions state in part:

"Comparisons of these [A_B / A_M] values with those obtained from the rules of the SAA Steel Structures Code [AS 1250 - 1972] indicate that the brace strength rule is conservative and the brace stiffness rule is inadequate."

That is, it seems that Mutton & Trahair were arguing that the stiffness rule in AS 1250 should be made even more rigorous. It is interesting, then, that the AS 4100 committee concluded that:

"A stiffness requirement is not given even though there is a theoretical solution (Ref. 27). This follows the finding (Ref. 28) that the requirements for centrally braced columns are satisfied by practical braces which satisfy the 2.5% rule."

 

[apsix]

Thanks sdz.

It does say "the Code brace strength requirements always govern the design of the brace, and the inadequacy of the stiffness requirements is unimportant".

But, as I read it, the only restraint being addressed is a brace acting as a strut or tie (axial force) connected to a rigid point at the far end. In that case I'm happy to believe that strength requirements govern.

What seems to be ignored are the cases where restraint is provided by bending or similar, as exampled by jhardy above, where displacement is likely to be significant.

The fact that this is ignored in both the Standard and the Commentary is disappointing.