COMBINED TENSION AND SHEAR LOAD
Parabolic
Calculations Utilization β N , V
[%]
Calculations 318-14 Chapter 17 Provision Comments for PROFIS Engineering Utilization β N , V
[%]
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 . Any other 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
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
)
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
* highest loaded anchor ** Anchor group ( relevant anchors )
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 the parabolic equation defined in Fig . R17.6 as follows :
β N , V
= ( β N ) 5 / 3 + ( β V
) 5 / 3
= ( 0.51 ) 5 / 3 + ( 0.6 ) 5 / 3 = 0.752
5 Combined tension and shear loads
β NV
= β N
E β N β V
E
Utilization β N [%]
Status 0.693 0.475 5 / 3 84 OK
+ β V
E
< = 1
Reference the PROFIS Engineering design guide section on the trilinear interaction equation for additional information about PROFIS Engineering interaction calculations .
355 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-14 Provisions