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L in deflection criteria

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I think that before we discuss what "L" is, we should look at what the 
deflection criteria represents, or is supposed to represent.

L/360 is the deflection limitation below which a brittle finish, i.e., 
plaster, will generally not crack.

L/240 is the deflection limitation below which deflection, i.e., sagging, 
will generally not be perceptible to the naked eye.

Presumably, these limitations were developed based on simple spans as they 
have been in existence for more years than I have been an engineer or 
studying to be an engineer (40+ years).

In that regard, "L" should be the distance between points of inflection.  
With regard to a cantilever, the question is much more complex.  "L" equal to 
twice the cantilever length would be a conservative assumption since the 
deflection of the cantilever is the result of the load on the cantilever 
*plus* the deflection due to rotation of the beam at the cantilever support.  
If the beam with two cantilevers would have an upward deflection between 
supports, such as when the cantilevers are loaded and the center span is not, 
"L" would be the span from support to support.

Probably more important than the precise value of "L" is determining what 
loads are to be used in calculating deflections.  The requirements of the UBC 
(Table 16-D, 1997 UBC) have, for non-cambered construction, been in error for 
as many years as I have been an engineer.  

Looking at what the deflection limitations are supposed to prevent, the L/360 
limitation would be the deflection that would occur *after* the brittle 
finish is applied, i.e., Live Load plus creep, plus partition loads, etc.  In 
essence, the loading for the deflection limitation for L/360 should be not 
less than LL+K(DL), where K is the percent of initial DL deflection that 
represents the creep that would occur after the brittle finish is applied.

In non-cambered construction, the loading for the L/240 limitation should be 
not less than LL+(1+K)DL.

Unless ponding is a problem, deflection, in and of itself, is a 
serviceability question and does not really affect the structural adequacy of 
a member.

Hope this helps.

A. Roger Turk, P.E.(Structural)
Tucson, Arizona

Marlou wrote:

. > When you have a beam with two cantilevers, one on the left and one on the
. > right.  What does people use as the L in L/240 or L/360 criteria.  I 
. > tried to look for a proper definition of L and it gave me that L is 
. > between two zero moments.
. > 
. > What is the correct L should we use.
. > 
. > 
. > Marlou
. >