Engineering analysis + design software

User Area > Advice

Wood-Armer Assessment [MUtil(T) and MUtil(B)]

While the Wood-Armer 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 two-way 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 pre-determined field of moments" (R H Wood, Concrete 1968) Eqn 7, we see that the slab is "safe" where

M*x(B)=Mx+K|Mxy| 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 Wood-Armer 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 in-plane forces N*x, N*y, Util(T), Util(B) etc.

Other Wood-Armer related topics

innovative | flexible | trusted

LUSAS is a trademark and trading name of Finite Element Analysis Ltd. Copyright 1982 - 2022. Last modified: May 21, 2024 . Privacy policy. 
Any modelling, design and analysis capabilities described are dependent upon the LUSAS software product, version and option in use.