COMBINED TENSION AND SHEAR LOAD
Parabolic
Variables β V
Variables ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering
β V
R17.8 — Tension and Shear Interaction The tension-shear interaction expression has traditionally been expressed as
N ua
N n ζ
+
V ua ζ
≤ 1.0
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 .
Excerpt from Table 17.5.2 showing the shear failure modes considered in ACI 318-19 anchoring-to-concrete provisions .
Table 17.5.2 — Design strength requirements of anchors
Failure Mode Single Anchor
V n
Individual anchor in a Group
Steel strength in shear ( 17.7.1 ) ϕV sa ≥ V ua ϕV sa
≥ V ua , i
Concrete breakout strength in shear ( 17.7.2 )
Concrete pryout strength in shear ( 17.7.3 ) ϕV cb
≥ V ua
ϕV cp
≥ V ua
Anchor Group
Anchors as a group
ϕV cbg
≥ V ua , g
ϕV cpg
≥ V ua , g
Part 4 of the PROFIS Engineering report shows the ratio of factored shear load ( V ua ) to shear design strength ( ϕV N ) via the parameter β V
. PROFIS Engineering calculates β V for each shear failure mode relevant to a particular anchor type .
Per ACI 318-19 Table 17.5.2 , the shear provisions of Chapter 17 are satisfied if all the calculated design strengths for shear failure modes are greater than or equal to the corresponding factored load . When PROFIS Engineering calculates β V
, it rounds up the result to the nearest whole number . The β V
-values given in Part 4 of the report correspond to a percentage . The PROFIS Engineering report shows “ OK ” under the Status heading if the
β V
-value is ≤ 100 %.
The highest βV-value corresponds to the “ controlling ” or “ governing ” failure mode in shear . This value is used as the shear component in the interaction equation . For the example below , all the calculated β V
-values are ≤ 100 %, and concrete edge failure in direction x + is the governing failure mode for shear because it has the highest utilization ( β V
= 60 %). The shear provisions of Chapter 17 have been satisfied . 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 *
Pryout ( bond strength controls )*
Concrete edge failure in direction x + **
* highest loaded anchor ** Anchor group ( relevant anchors )
N / A N / A N / A N / A
6,000 52,765 12 OK
6,000 10,080 60 OK
When V ua is greater than ϕV n
, the β V
-value will be greater than 100 %. The shear provisions of Chapter 17 are not satisfied when V ua is greater than ϕV n
. The PROFIS Engineering report shows “ not recommended ” under the Status heading if the β V
-value is ≥ 100 %.
For the example below , the β V
-value for concrete edge failure in direction x + is > 100 %; therefore , the PROFIS Engineering report shows “ not recommended ” under the Status heading for this failure mode to indicate that the Chapter 17 provisions have not been satisfied .
4 Shear load Load V ua
[ lb ]
Capacity ϕV n [ lb ]
Utilization
β N
= V ua / ϕV n
Status
Steel strength * 3,750 8,221 46 OK
Steel failure with lever arm *
Pryout ( bond strength controls )*
Concrete edge failure in direction x + **
* highest loaded anchor ** Anchor group ( relevant anchors )
N / A N / A N / A N / A
15,000 76,400 20 OK
15,000 11,592 130 not recommended
Reference the PROFIS Engineering design guide section on β N for additional information about PROFIS Engineering interaction calculations .
343 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions