COMBINED TENSION AND SHEAR LOAD
Tri-Linear
Variables Utilization E
Variables 318-14 Chapter 17 Provision Comments for PROFIS Engineering
E 17.6 – Interaction of tensile and shear forces
Unless determined in accordance with 17.3.1.3 , anchors or groups of anchors that are subjected to both shear and axial loads shall be designed to satisfy the requirements of 17.6.1 through 17.6.3 . The values of ϕN n and ϕV n shall be the required strengths as determined from 17.3.1.1 or from
17.2.3 . 17.6.1 If V ua
/( ϕV n ) ≤ 0.2 for the governing strength in shear , then full strength in tension shall be permitted : ϕN n ≥ N u a .
17.6 . 2 If N ua /( ϕN n
) ≤ 0.2 for the governing strength in tension , then full strength in shear shall be permitted : ϕV n ≥ V ua
.
17.6.3 If V ua /( ϕV n
) > 0.2 for the governing strength in shear and N ua /( ϕN n
) > 0.2 for the governing strength in tension , then
N ua + V ua ≤ 1 . 2 ( 17 . 6 . 3 ) ϕN n ϕV n
R17.6 – Interaction of tensile and shear forces The shear-tension interaction expression has traditionally been expressed as
N ua
N n
E
+
where E varies from 1 to 2 . The current trilinear recommendation is a simplification of the expression where E = 5 / 3 . The limits were chosen to eliminate the requirement for computation of interaction effects where very small values of the second force are present . Another interaction expression that is verified by test data , however , can be used to satisfy 17.3.1.3 .
V ua
V n
E
≤ 1.0
ACI 318-14 anchoring-to-concrete provisions default to what is known as a trilinear interaction equation , which is given in Eq . ( 17.6.3 ). PROFIS Engineering checks both Eq . ( 17.6.3 ) and the parabolic interaction equation given in the ACI 318-14 commentary R17.6 . 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 R17.6 permits the governing tension component ( N ua
/ ϕN N ) and the governing shear component ( V ua
/ ϕV N
) to be raised to any power ( E ) between 1 and 2 . When checking combined tension / shear interaction with Eq . ( 17.6.3 ), the governing tension component ( N ua
/ ϕN N ) and the governing shear component ( V ua / ϕV N
) are not raised to any power , so E = 1.0 .
Below is an example of how the PROFIS Engineering report shows the parameters used in the tri-linear interaction equation ( 17.6.3 ).
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 ( E ) when Eq . ( 17.6.3 ) is used , the parameter “ E ” is shown as 1.0 in the report . The parameter “ Utilization
β N , V
” is calculated as follows :
Example : β N , V
= ( β N ) 1.0 + ( β V
) 1.0 ≤ 1.2 Eq . ( 17.6.3 )
|
β N , V
= ( β N + β V
)/ 1.2 ≤ 1.0
|
PROFIS Engineering |
= ( 0.693 + 0.475 )/ 1.2 = 0.973 |
β N , V
< 1.0
|
OK |
5 Combined tension and shear loads
β N β V
E
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 .
363 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-14 Provisions