COMBINED TENSION AND SHEAR LOAD
Parabolic
Variables ζ
Variables ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering ζ
R17.8 — Tension and Shear Interaction The tension-shear interaction expression has traditionally been expressed as
N ua
N n ζ
+
where ζ varies from 1 to 2 . The current trilinear recommendation is a simplification of the expression where ζ = 5 / 3 . The limits were chosen to eliminate the requirement for calculation of interaction effects where very small values of the second force are present . Any other interaction expression that is verified by test data , however , can be used to satisfy 17.5.2.3 .
V ua
V n ζ
≤ 1.0
ACI 318-19 anchoring-to-concrete provisions default to what is known as a trilinear interaction equation , which is given in Eq . ( 17.8.3 ). PROFIS Engineering checks both Eq . ( 17.8.3 ) and the parabolic interaction equation given in the ACI 318-19 commentary R17.8 . The PROFIS Engineering report shows the most favorable results .
The failure mode for a given tension or shear load condition can be expressed as a ratio of factored load to design strength :
• factored tension load / tension design strength = ( N ua / ϕN N
)
• factored shear load / shear design strength = ( V ua / ϕV N
).
The “ governing ” failure mode can be defined as the highest ( factored load / design strength ) ratio for the failure modes being considered . The generalized interaction equation given in the commentary R17.8 permits the governing tension component ( N ua
/ ϕN N ) and the governing shear component ( V ua
/ ϕV N
) to be raised to any power ( ζ ) between 1 and 2 . When PROFIS Engineering checks combined tension / shear interaction with the parabolic equation , the governing tension component ( N ua
/ ϕN N ) and the governing shear component ( V ua
/ ϕV N
) are raised to the 5 / 3 power , so ζ = 5 / 3 .
Below is an example of how the PROFIS Engineering report shows the parameters used in the parabolic interaction equation . The parameter “ β N
” corresponds to the governing tension component ( N ua / ϕN N
) and the parameter “ β V ” corresponds to the governing shear component ( V ua / ϕV N
). Since ( N ua / ϕN N
) and ( V ua / ϕV N
) are each raised to the 5 / 3 power when the parabolic equation is used , the parameter “ ζ ” is shown as 5 / 3 in the report . The parameter “ Utilization β N , V
” is calculated as follows : β N , V
= ( β N ) 5 / 3 + ( β V
) 5 / 3 ≤ 1.0 Fig . R17.8
|
β N , V
= ( β N ) 5 / 3 + ( β V
) 5 / 3 ≤ 1.0
|
PROFIS Engineering |
= ( 0.693 ) 5 / 3 + ( 0.475 ) 5 / 3 = 0.832 |
β N , V
< 1.0
|
OK |
Reference ACI 318-19 Fig . R17.8 .
5 Combined tension and shear loads
β NV
= β N ζ β N β V ζ
Utilization β N [%]
Status 0.693 0.475 5 / 3 84 OK
+ β V ζ
< = 1
Reference the PROFIS Engineering design guide section on the trilinear interaction equation for additional information about PROFIS Engineering interaction calculations .
345 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions