COMBINED TENSION AND SHEAR LOAD
Tri-Linear
Variables ζ
Variables ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering ζ
17.8 — Tension and shear interaction 17.8.1 Unless tension and shear interaction effects are considered in accordance with 17.5.2.3 , anchors or anchor groups that resist both tension and shear shall satisfy 17.8.2 and 17.8.3 . The values of ϕN n and ϕV n shall be in accordance with 17.5.2 or 17.10 .
17.8 . 2 It shall be permitted to neglect the interaction between tension and shear if ( a ) or ( b ) is satisfied .
( a ) N ua /( ϕN n
) ≤ 0.2 ( 17.8 . 2a )
( b ) V ua /( ϕV n
) ≤ 0.2 ( 17.8 . 2b )
17.8.3 If N ua /( ϕN n
) > 0.2 for the governing strength in tension and V ua /( ϕV n
) > 0.2 for the governing strength in shear , then Eq . ( 17.8.3 ) shall be satisfied . N ua +
V ua ≤ 1 . 2 ( 17 . 8 . 3 ) ϕN n
R17.8 – Tension and Shear Interaction The tension-shear interaction expression has traditionally been expressed as
N ua
N n ϕV 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 checking combined tension / shear interaction with Eq . ( 17.8.3 ), the governing tension component ( N ua
/ ϕN N ) and the governing shear component ( V ua / ϕV N
) are not raised to any power , so ζ = 1.0 .
Below is an example of how the PROFIS Engineering report shows the parameters used in the tri-linear interaction equation ( 17.8.3 ). 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 not raised to any power ( ζ ) when Eq . ( 17.8.3 ) is used , the parameter “ ζ ” is shown as 1.0 in the report . The parameter “ Utilization β N , V
” is calculated as follows : β N , V
= ( β N ) 1.0 + ( β V
) 1.0 ≤ 1.2 Eq . ( 17.8.3 ) β N , V
= ( β N + β V
)/ 1.2 ≤ 1.0 = ( 0.693 + 0.475 )/ 1.2
5 Combined tension and shear loads
PROFIS Engineering
= 0.973 β N , V < 1.0 OK β N β V ζ Utilization β N
[%] Status 0.693 0.475 1.000 0.973 OK β NV
= ( β N + β V
) 1.2 < = 1
Reference the PROFIS Engineering design guide section on the parabolic interaction equation for additional information about PROFIS Engineering interaction calculations .
Reference ACI 318-19 Fig . R17.8 .
354 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions