COMBINED TENSION AND SHEAR LOAD
Tri-Linear
Equations β NV = ( β N
+ β V
)/ 1.2 ≤ 1
Equations ACI 318-19 Chapter 17 Provision Comments for PROFIS Engineering β NV
= ( β N + β V
)/ 1.2 ≤ 1
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 ) ϕ n ϕV n
Excerpt from Table 17.5.2 showing the tension failure modes considered in ACI 318-19 anchoringto-concrete provisions .
Table 17.5.2 — Design strength requirements of anchors
Failure Mode Single Anchor
Individual anchor in a Group
Steel strength in tension ( 17.6.1 ) ϕN sa ≥ N ua ϕN sa
≥ N ua , i
Concrete breakout strength in tension ( 17.6 . 2 ) ϕN cb
≥ N ua
Pullout strength in tension ( 17.6.3 ) ϕN pn ≥ N ua ϕN pn
≥ N ua , i
Concrete side-face blowout strength in tension ( 17.6.4 )
Bond strengh of adhesive anchor in tension ( 17.6.5 ) ϕN sb
≥ N ua
ϕN a
≥ N ua
Anchor Group
Anchors as a group
ϕN cbg
≥ N ua , g
ϕN sbg
≥ N ua , g
ϕN ag
≥ N ua , g
ACI 318-19 anchoring-to-concrete provisions default to what is known as a trilinear interaction equation , which is given in Eq . ( 17.8.3 ). PROFIS Engineering checks both Eq . ( 17.8.3 ) and the parabolic interaction equation given in the ACI 318-19 commentary R17.8 . 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 . Section 17.8.2 permits the interaction check defined by Eq . ( 17.8.3 ) to be waived if either ( a ) N ua
/( ϕN n
) ≤ 0.2 for the “ governing ”, i . e . “ highest ”, ( factored tension load / tension design strength ) ratio , or ( b ) V ua
/( ϕV n
) ≤ 0.2 for the “ governing ”, i . e . “ highest ”, ( factored shear load / shear design strength ) ratio is satisfied . Per Section 17.8.3 , if the provisions in Section 17.8.2 and cannot be satisfied ; combined tension / shear interaction is checked per Eq . ( 17.8.3 ). PROFIS Engineering defines the calculated results for Eq . ( 17.8.3 ) via the parameter “ β NV
”.
Part 3 of the PROFIS Engineering report shows the ratio of factored tension load ( N ua
) to tension design strength ( ϕN N ) via the parameter β N
. For the example below , concrete breakout failure is the governing failure mode for tension because it has the highest utilization ( β N
= 51 %).
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 )
349 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-19 Provisions