COMBINED TENSION AND SHEAR LOAD
Tri-Linear
Variables Utilization β N
Variables 318-14 Chapter 17 Provision Comments for PROFIS Engineering
β N
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 )
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
. PROFIS Engineering calculates β N for each tension failure mode relevant to a particular anchor type .
Per ACI 318-14 Table 17.3.1.1 , the tension provisions of Chapter 17 are satisfied if all the calculated design strengths for tension failure modes are greater than or equal to the corresponding factored load . When PROFIS Engineering calculates
β N
, it rounds up the result to the nearest whole number . The β N
-values given in Part 3 of the report correspond to a percentage . The PROFIS Engineering report shows “ OK ” under the Status heading if the β N
-value is < 100 %.
The highest β N
-value corresponds to the “ controlling ” or “ governing ” failure mode in tension . This value is used as the tension component in Eq . ( 17.6.3 ). For the example below , all the calculated β N
-values are ≤ 100 %, and concrete breakout failure is the governing failure mode for tension because it has the highest utilization ( β N
= 51 %). The tension provisions of Chapter 17 have been satisfied . ϕ 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 tension ( 17.4.1 ) ϕN sa ≥ N ua ϕN sa
≥ N ua , i
Concrete breakout strength in tension ( 17.4.2 ) ϕN cb
≥ N ua
Pullout strength in tension ( 17.4.3 ) ϕN pn ≥ N ua ϕN pn
≥ N ua , i
Anchor Group
Anchors as a group
ϕN cbg
≥ N ua , g
Example : 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 )
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Concrete side-face blowout strength in tension ( 17.4.4 )
Bond strengh of adhesive anchor in tension ( 17.4.5 )
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ϕN sb
≥ N ua
ϕN a
≥ N ua
|
ϕN sbg
≥ N ua , g
ϕN ag
≥ N ua , g
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When N ua is greater than ϕN n
, the β N
-value will be greater than 100 %. The tension provisions of Chapter 17 are not satisfied when N ua is greater than ϕN n
. The PROFIS Engineering report shows “ not recommended ” under the Status heading if the β N
-value is > 100 %.
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For the example below , the β N
-values for bond strength and concrete breakout failure are > 100 %; therefore , the PROFIS Engineering report shows “ not recommended ” under the Status heading for these failure modes to indicate that the Chapter 17 provisions have not been satisfied .
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360 NORTH AMERICAN PROFIS ENGINEERING ANCHORING TO CONCRETE DESIGN GUIDE — ACI 318-14 Provisions