User Area > Advice
WoodArmer Assessment [MUtil(T) and
MUtil(B)]
While the WoodArmer principles have been rationalised to a
few basic equations in order to enable efficient design, it is
sometimes necessary to consider arrangements of reinforcement
which have design strengths based on a different
rationale. A
typical application is the assessment of an existing structure.
LUSAS is able to assess slabs and report if they are
"safe" (factor of safety >1) or "unsafe"
(fos<1) for reinforcement in the top and bottom of the slab.
LUSAS in fact reports MUtil which is equal to the reciprocal of
the safety factor.
For a typical twoway spanning slab with sagging in the X and
Y directions, efficient design may be based on
M*x(B)=Mx+Mxy and M*y(B)=My+Mxy
and following
procedure
However, with reference to "The reinforcement of slabs
in accordance with a predetermined field of moments" (R H
Wood, Concrete 1968) Eqn 7, we see that the slab is
"safe" where
M*x(B)=Mx+KMxy and M*y(B)=My+Mxy/K
where K is a positive constant
When MUtil(B) is selected in LUSAS
Modeller, moment
capacities in the X and Y directions must be given; let us call
them MRx(B) and MRy(B). LUSAS will assess the possible values of
M*x(B) and M*y(B) for a variety of values of K. If there exists
a value of K for which MRx>M*x and MRy>M*y then the slab
is "safe" i.e. M*x/MRx<1 and M*y/MRy<1. The
highest available ratio of M*x/MRx or M*y/MRy is reported at each
node.
Values for top surface moments of resistance are designed to
resist hogging and should be positive, bottom surface values are
designed to resist sagging and should be negative.
The calculation may be demonstrated by using the example given
on the WoodArmer
page.
At node 122, Mx=3.769, My=2.613,
Mxy=2.378.
Suppose that MRx=4.958 and MRy=7.369
If many values of K are tried, it will be found that when
K=0.5,
M*x=(Mx+0.5*Mxy)=4.958 and M*y=(My+2*Mxy)=7.369
and MUtil(B)=1
Suppose that MRx=3.827 and MRy=100
If many values of K are tried, it will be found that when
K=0.024418,
M*x=(Mx+0.024*Mxy)=3.827 and M*y=(My+Mxy/0.024)=100
and MUtil(B)=1
Suppose that MRx=5 and MRy=10
Clearly there exists a value of K for which M*x/MRx<1 and
M*y/MRy<1
This value has not been checked explicitly, but LUSAS reports
MUtil(B)=0.9241 (factor of safety = 1.082)
The same principles apply for inplane forces N*x, N*y,
Util(T), Util(B) etc.
Other WoodArmer
related topics
