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Stress Ratio, also termed Utilization Factor, is defined
in CAST as the ratio
of stress demand to stress limit.
For Concrete Struts and Nodes, the Stress Ratio is defined as
where:
 |
= |
Strut stress or Node side (perpendicular) stress, |
|
= |
strength reduction factor, |
 |
= |
effective strength =  , |
 |
= |
specified compressive strength of concrete, and |
 |
= |
efficiency factor. |
For Non-Prestressed Reinforcement Ties, the Stress Ratio is given as 
where:
|
= |
Tie stress, |
 |
= |
yield strength of non-prestressed
reinforcement, and |
 |
= |
yield overstrength of non-prestressed reinforcement. |
fc' Ratio is defined as the ratio of stress demand to the
specified compressive strength of concrete or
Beta Ratio is defined as the ratio of stress demand to 
or
Notes:
- A design is acceptable if all Stress Ratios in the Struts,
Ties, and Nodes are less than 1.0. Struts, Ties, and Nodes whose
Stress Ratios are greater than 1.0 are declared
overstressed (O/S). Please note that merely satisfying all
Stress Ratios in Struts, Ties, and Nodes is not enough. The
design also has to satisfy equilibrium; however, this
requirement is automatically satisfied if your truss
analysis is successful. In addition, all Strut and Tie
Effective Widths and Node dimensions have to be located within the
Boundaries. A good design also has to consider
serviceability requirement to avoid excessive deformation
and cracks. The last requirement can be implicitly satisfied
if the selected Strut-and-Tie Model follows the elastic
solution.
- The stress demand for Concrete Struts and Nodes is given
as
where:
 |
= |
Strut force or force acting on a Node side, |
|
= |
D-Region thickness, and |
|
= |
Strut Effective Width or Node side (perpendicular) width. |
- The stress demand for Non-Prestressed Reinforcement Ties
is given as
where:
|
= |
Tie force and |
|
= |
cross-sectional area of non-prestressed reinforcement. |
 |
= |
beta factor for Struts and |
|
= |
beta factor for Nodes. |
Click
here to see summary of
and
defined in ACI Code.
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