COMBINED TENSION AND SHEAR LOAD
Tri-Linear
Calculations Utilization β N , V
[%]
Calculations ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering Utilization β N , V
[%]
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 ϕV n
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
/ ϕV1 ).
PROFIS Engineering references these ratios as “ utilizations ”, and shows them in the report as a percentage .
Part 3 of the PROFIS Engineering report shows the utilizations for each tension failure mode being considered and designates “ tension utilizations ” via the parameter “ β N
”. 3 Tension load
Load N ua [ lb ]
Capacity
ϕN n
[ lb ]
Utilization
β N
= N ua / ϕN n
Status
Steel strength * 5,000 14,550 35 OK Bond strength ** 10,000 31,564 32 OK Sustained tension load bond strength * 3,450 16,800 21 OK Concrete breakout Failure ** 10,000 19,971 51 OK
* highest loaded anchor ** Anchor group ( anchors in tension )
Part 4 of the PROFIS Engineering report shows the utilizations for each shear failure mode being considered and designates “ shear utilizations ” via the parameter “ β V
”.
4 Shear load
Load V ua [ lb ]
Capacity
ϕV n
[ lb ]
Utilization
β N
= V ua / ϕV n
Status
Steel strength * 1,500 4,540 33 OK Steel failure with lever arm * N / A N / A N / A N / A Pryout ( bond strength controls )* 6,000 52,765 12 OK Concrete edge failure in direction x + ** 6,000 10,080 60 OK
The “ governing ” failure mode can be defined as the highest utilization for the failure modes being considered . PROFIS Engineering designates the sum of the utilization for the governing failure mode in tension and the utilization for the governing failure mode in shear as “ β N , V
”, and shows it as a percentage in Part 5 of the report .
For the examples above , concrete breakout failure is the governing tension failure mode ( β N
= 51 %) and concrete edge failure in direction x + is the governing shear failure mode ( β V
= 60 %). PROFIS Engineering would calculate β N , V per Eq . ( 17.8.3 ) as follows :
β N , V
= ( β N + β V
)/ 1.2 = ( 0.51 + 0.6 )/ 1.2 = 0.925
5 Combined tension and shear loads
β N β V ζ Utilization β N
[%] Status 0.510 0.600 1.000 0.925 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 .
355 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions