COMBINED TENSION AND SHEAR LOAD
Tri-Linear
Variables Utilization β V
Variables 318-14 Chapter 17 Provision Comments for PROFIS Engineering
β V
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 ua
.
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
Table 17.3.1.1 — Required strength of anchors , except as noted in 17.2.3
Failure Mode ϕV n
Single Anchor
Individual anchor in a Group
Steel strength in shear ( 17.5.1 ) ϕ steel
V sa
≥ V ua ϕ steel
V sa
≥ V ua , i
Concrete breakout strength in shear ( 17.5 . 2 )
Concrete pryout strength in shear ( 17.5.3 ) ϕ concrete
V cb
≥ V ua ϕ concrete
V cp
≥ V ua
Anchor Group
Anchors as a group
ϕ concrete
V cbg
≥ V ua , g ϕ concrete
V ag
≥ V ua , g
The PROFIS Engineering anchor portfolio includes post-installed mechanical anchors , postinstalled adhesive anchors , and cast-anchors . The following shear failure modes are considered for each type of anchor :
post-installed mechanical anchor steel strength : concrete breakout strength : concrete pryout strength :
post-installed adhesive anchor steel strength : concrete breakout strength : concrete pryout strength :
cast-in anchor steel strength : concrete breakout strength : concrete pryout strength : β V
= V ua ( i ) / ϕ steel
V sa β V
= V ua ( i ) / ϕ concrete
V cb or β V = V ua ( g )
/ ϕ concrete
V cbg β V
= V ua ( i ) / ϕ concrete
V cp or β V = V ua ( g )
/ ϕ concrete
V cpg β V
= V ua ( i ) / ϕ steel
V sa β V
= V ua ( i ) / ϕ concrete
V cb or β V = V ua ( g )
/ ϕ concrete
V cb g β V
= V ua ( i ) / ϕ concrete
V cp or β V = V ua ( g )
/ ϕ concrete
V cpg β V
= V ua ( i ) / ϕ steel
V s a β V
= V ua ( i ) / ϕ concrete
V cb or β V = V ua ( g )
/ ϕ concrete
V cbg β V
= V ua ( i ) / ϕ concrete
V cp or β V = V ua ( g )
/ ϕ concrete
V cpg where V ua ( i ) corresponds to the highest factored shear load acting on an individual anchor and V ua ( g ) corresponds to the total factored shear load acting on a group of anchors .
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 318-14 Table 17.3.1.1 , 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 β V
-value corresponds to the “ controlling ” or “ governing ” failure mode in shear . This value is used as the shear component in Eq . ( 17.6.3 ). 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 .
Example : 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 )
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 .
Example : 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 .
362 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-14 Provisions