EXAMPLE CALCULATION Mechanical Anchors (ACI 318 App. D/ICC-ES AC193) Example calculation for a single Strong-Bolt™ anchor using USD: Determine if a single ¹⁄₂" diameter Strong-Bolt ™ torque-controlled expansion anchor with a minimum 5" embedment (h ( h ef = 4¹⁄₂ inches) installed 4" from the edge of a 12" deep spandrel beam is adequate for a service tension load of 1,000 lb. for wind and a reversible service shear load of 350 lb. for wind. The anchor will be in the tension zone, away from other anchors in ƒ'c = 3,000 psi normal-weight concrete.
1000 lb. 350 lb. 4¹⁄₂"
4"
Reference the appropriate tables in this catalog for Strong-Bolt anchor performance values as determined from testing in accordance with ACI 355.2 and ICC-ES AC193.
CALCULATIONS CALCULATION S AND DISCUSSION
REFERENCE
Note: Calculations are performed in accordance with ACI 318-05. 1. Determine the factored tension and shear design loads:
ACI 318, 9.2.1
N ua = 1.6W 1.6 W = = 1.6 x 1,000 = 1,600 lb.
Note: Rebar not shown for clarity.
CALCULATIONS CALCULATIO NS AND DISCUSSION
4. Concrete breakout capacity under tension loading:
D.5.2
φN cb ≥ N ua N cb =
V ua = 1.6W 1.6 W = = 1.6 x 350 = 560 lb.
REFERENCE
Eq. (D-1)
ANc ψ ψ ψ N ANco ed,N c,N cp,N b
Eq. (D-4);
where: 2. Design considerations:
D.4.1.2
Eq. (D-7)
substituting:
This is a combined tension and shear interaction problem where values for both φN n and φV n need to be determined. φN n is the lesser of the design tension strength controlled by: steel ( φN sa ), concrete breakout (φN cb ), or pull-out ( φnN pn ). φV n is the lesser of the design shear strength controlled by: steel ( φV sa ), concrete breakout (φV cb ), or pryout ( φV cp ).
3. Steel capacity under tension Loading:
N b = k c √ƒ ' 'c h ef 1.5
φN cb = φ ANc ψ ed,N ψ c,N ψ cp,N k c √ƒ ' 'c h ef 1.5 ANco
where:
D.5.1
k c = k cr = 17 (Anchor is installed in a tension zone, therefore, cracking is assumed at service loads
This catalog
ψ cp,N = 1.0
D.5.2.7 Eq. (D-11)
φN sa ≥ N ua
Eq. (D-1)
ψ = 0.7 + 0.3 c a,min when c ed,N a,min < 1.5 h ef 1.5h 1.5 h ef
N sa = 13,500 lb.
This catalog
by observation, c a,min = 4 < 1.5h 1.5 h ef
φ = 0.75
This catalog
ψ ed,N = 0.7 + 0.3
n = n = 1 (single anchor)
(4) 1.5(4.5)
= 0.88
Calculating for φN sa :
ψ c,N = 1.0 assuming cracking
φN sa = 0.75 x 1 x 13,500 = 10,125 lb. > 1,600 lb. – OK
at service loads (ft > fr)
D.5.2.6
φ = 0.65 for Condition B
This catalog
∴ ¹⁄₂ in. diameter anchor is adequate
(no supplementary reinforcement provided) ANco = 9h 9h ef 2 = 9(4.5) 2 = 182.25 in. 2
Eq. (D-6)
ANc = (ca 1 + 1.5h 1.5 h ef )(2 x 1.5h 1.5h ef ) = (4 + 1.5(4.5))(2 x 1.5(4.5)) = 145.13 in. 2
Fig. RD.5.2.1(a)
ANc 145.13 = = 0.8 ANco 182.25 Calculating for φN cb : Would you like help with these c alculations? Visit www.simpsonanchors.com to download the Simpson Strong-Tie ® Anchor Designer ™ software.
24
φN cb = 0.65 x 0.8 x 1.0 x 0.88 x 1.0 x 17 x √3,000 x (4.5) 1.5 = 4,067 lb. > 1,600 lb. – OK
Continued on next page.
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EXAMPLE CALCULATION Mechanical Anchors (ACI 318 App. D/ICC-ES AC193) Continued from previous page. CALCULATIONS AND DISCUSSION
REFERENCE
5. Pullout capacity:
D.5.3
CALCULATIONS AND DISCUSSION
REFERENCE
9. Concrete pryout strength:
D.6.3
Pullout capacity, N pn,cr , is established by reference tests in cracked concrete by the reliability test of ACI 355.2. Data from the anchor prequalification testing must be used. Reference Strong-Bolt ™ anchor "characteristic tension design values" table for the 5 percent fractile value, N pn,cr.
φnV cp ≥ V ua
Eq. (D-2)
V cp = k cp N cb
Eq. (D-29)
φN pn ≥ N ua
n = 1
Eq. (D-1)
N pn,cr = 2,995 x
3,000 ( 2,500 )
0.5
= 3,281 lb.
This catalog
k cp = 2.0 and φ = 0.70 4,067 = 12,514 lb. k cp N cb = 2.0 x 0.65
D.4.1.2
φnV cp = 0.70 x 1 x 12,514 = 8,760 lb. > 560 lb.
This catalog
φ = 0.65 φN pn = 0.65 x 3,281 = 2,133 lb. > 1,600 lb.
–
OK
6. Check all failure modes under tension loading:
where:
Summary: Steel capacity = 10,125 lb. Concrete breakout capacity = 4,067 lb. Pullout capacity = 2,133 lb. ← Controls ∴ φN n = 2,133 lb. as pullout capacity controls
This catalog D.6.3.1 –
OK
10. Check all failure modes under shear Loading:
D.4.1.2
Summary: Steel capacity
= 4,264 lb.
D.6.1
φV sa ≥ V ua
Concrete breakout capacity = 2,301 lb. ← Controls
Eq. (D-2)
Pryout capacity
V sa = 6,560 lb.
This catalog
∴ φV n = 2,301 lb. as concrete breakout capacity controls
7. Steel capacity under shear loading:
φ = 0.65
This catalog
= 8,760 lb.
Calculating for φV sa :
φV sa = 0.65 x 6,560 = 4,264 lb. > 560 l b.
–
11. Check interaction of tension and shear forces:
OK
∴ ¹⁄₂ in. diameter anchor is adequate 8. Concrete breakout capacity under shear loading:
φV cb ≥ V ua V cb =
AVc ψ ψ ed,V c,V V b AVco
D.6.2
If 0.2 φV n ≥ V ua, then the full tension design strength is permitted.
Eq. (D-2)
By observation, this is not the case.
Eq. (D-21)
If 0.2 φN n ≥ N ua , then the full shear design strength is permitted
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(d o e )
D.7.1
D.7.2
By observation, this is not the case.
where: V b = 7
D.7
0.2
√d o √ƒ 'c c a11.5
Eq. (D-24)
substituting: φV cb = φ AVc ψ ed,V ψ c,V 7 e AVco d o
( )
Therefore: N ua V + ua ≤ 1.2 φN n φV n
0.2
√d o √ƒ 'c c a11.5
Eq. (D-31)
1,600 560 + = 0.75 + 0.24 = 0.99 < 1.2 2,133 2,301
where:
–
OK
φ = 0.70 for Condition B (no supplementary reinforcement provided)
D4.4(c)(i)
AVco = 4.5ca 12 = 4.5(4) 2 ∴ AVco = 72 in. 2
Eq. (D-23)
AVc = 2(1.5c a 1)(1.5ca 1) = 2(1.5(4))(1.5(4)) ∴ AVc = 72 in. 2 72 AVc = =1 AVco 72
Fig. RD.6.2.1(a)
ψ ed,V = 1.0 since c a 2 > 1.5c a 1
Eq. (D-27)
12. Summary A single ¹⁄₂" diameter Strong-Bolt anchor at a 5" embedment depth is adequate to resist the applied service tension and shear loads of 1,000 lb. and 350 lb., respectively. ™
D.6.2.1
ψ c,V = 1.0 assuming cracking at service loads (ft > fr)
D.6.2.7
d o = 0.5 in. e = 8d 0 = 8 (0.5) = 4"
D.6.2.2
ca 1 = 4 in.
φV cb = 0.70 x 1 x 1.0 x 1.0 x 7 x
( 0.54 )
0.2
x √0.5
x √3,000 x (4) 1.5 = 2,301 lb. > 560 lb.
–
OK
25
EXAMPLE CALCULATION Adhesive Anchors (ICC-ES AC308) Example calculation for a single SET-XP™ epoxy adhesive anchor using USD: Determine if a single ¹⁄₂" diameter ASTM A193 Grade B7 anchor rod in SET-XP ™ epoxy adhesive anchor with a minimum 4 ¹⁄₂" embedment (h ef = 4¹⁄₂") installed 1³⁄₄" from the edge of a 12" deep spandrel beam is adequate for a service tension load of 560 lb. for wind and a reversible service shear load of 425 lb. for wind. The anchor will be in uncracked dry concrete, away from other anchors in ƒ'c = 3,000 psi normal-weight concrete. The anchor will be subjected to a maximum short-term temperature of 110˚F and a maximum long-term temperature of 75 ˚F. Continuous inspection will be provided
560 lb. 425 lb. 4¹⁄₂"
1³⁄₄"
Note: Rebar not shown for clarity.
Reference the appropriate tables in this catalog f or SET-XP epoxy adhesive anchor performance values as determined from testing in accordance with ICC-ES AC308. CALCULATIONS AND DISCUSSION
REFERENCE
Note: Calculations are performed in accordance with ICC-ES AC308 and ACI 318-05. 1. Determine the factored tension and shear design loads:
CALCULATIONS AND DISCUSSION
REFERENCE
4. Concrete breakout capacity under tension loading:
D.5.2
φN cb ≥ N ua ACI 318, 9.2.1 N cb =
N ua = 1.6W = 1.6 x 560 = 900 lb. V ua = 1.6W = 1.6 x 425 = 680 lb.
Eq. (D-1)
ANc ψ ψ ψ N ANco ed,N c,N cp,N b
where: N b = k c √ƒ 'c h ef 1.5
2. Design considerations:
D.4.1.2
This is a combined tension and shear interaction problem where values for both φN n and φV n need to be determined. φN n is the lesser of the design tension strength controlled by: steel ( φN sa ), concrete breakout (φN cb ), or adhesive ( φN a ). φV n is the lesser of the design shear strength controlled by: steel ( φV sa ), concrete breakout (φV cb ), or pryout ( φV cp ).
3. Steel capacity under tension loading:
Eq. (D-4);
Eq. (D-7)
substituting:
φN cb = φ ANc ψ ed,N ψ c,N ψ cp,N k c √ƒ 'c h ef 1.5 ANco
where: k c = k uncr = 24
This catalog
c a,min = 1.75" = c min – OK
D.5.1
c ac = 3h ef = 3(4.5) = 13.5" ψ cp,N = c a,min = 0.13 ≥ 1.5h ef = 0.5 c ac c ac
φN sa ≥ N ua
Eq. (D-1)
ψ cp,N = 0.5
N sa = 17,750 lb.
This catalog
ψ
φ = 0.75
This catalog
c a,min
when c a,min < 1.5 h ef ed,N = 0.7 + 0.3 1.5h ef
n = 1 (single anchor)
by observation, c a,min < 1.5h ef
Calculating for φN sa :
ψ ed,N = 0.7 + 0.3 1.75 = 0.78
φN sa = 0.75 x 1 x 17,750 = 13,313 lb. > 900 lb. – OK
This catalog Eq. (D-13)
Eq. (D-11)
1.5(4.5)
ψ c,N = 1.0 since k c = k uncr = 24
D.5.2.6
φ = 0.65 for Condition B
This catalog
(no supplementary reinforcement provided)
Would you like help with these calculations? Visit www.simpsonanchors.com to download the Simpson Strong-Tie ® Anchor Designer ™ software.
ANco = 9h ef 2 = 9(4.5) 2 = 182.25 in. 2
Eq. (D-6)
ANc = (ca 1 + 1.5h ef )(2 x 1.5h ef ) = (1.75 + 1.5(4.5))(2 x 1.5(4.5)) = 114.75 in. 2 ANc 114.75 = = 0.63 ANco 182.25
Fig. RD.5.2.1(a)
Calculating for φN cb :
φN cb = 0.65 x 0.63 x 1.0 x 0.78 x 0.5 x 24 x √3,000 x (4.5) 1.5 = 2,004 lb. > 900 lb. – OK
26
Continued on next page.
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EXAMPLE CALCULATION Adhesive Anchors (ICC-ES AC308) Continued from previous page. CALCULATIONS AND DISCUSSION
REFERENCE
CALCULATIONS AND DISCUSSION
REFERENCE
5. Adhesive anchor capacity under tension loading:
AC308 Section 3.3
8. Concrete breakout capacity under shear loading:
D.6.2
φN a ≥ N ua ANa ψed,Na ψ p,Na N ao N a = ANao
Eq. (D-1)
N ao = τk,uncr πdh ef = 2,422π(0.5)(4.5) = 17,120 lb.
Eq. (D-16f)
where:
Eq. (D-16d)
V b = 7
s cr,Na = 20d
√
τk,uncr ≤
1,450
s cr,Na = (20)(0.5)
√
Eq. (D-16a)
3h ef
AVc ψ ψ V AVco ed,V c,V b
V cb =
(d o e )
Eq. (D-21)
0.2
√d o √ƒ 'c c a11.5
Eq. (D-24)
( )
Eq. (D-16e)
0.2
√d o √ƒ 'c c a11.5
where:
φ = 0.70 for Condition B (no supplementary reinforcement provided)
D4.4(c)(i)
ANa = (c a1 + c cr,Na )(s cr,Na ) = (1.75 + 6.46)(12.92) = 106.07" 2 ψed,Na = (0.7 + 0.3 c a,min ) ≤ 1.0 Since c a,min < c cr,Na Eq. (D-16m) c cr,Na
AVco = 4.5ca 12 = 4.5(1.75) 2 ∴ AVco = 13.78 in. 2
Eq. (D-23)
ψed,Na = (0.7 + 0.3 c a,min ) = (0.7 + 0.3 1.75 ) = 0.78
AVc = 2(1.5c a 1)(1.5ca 1) = 2(1.5(1.75))(1.5(1.75)) ∴ AVc = 13.78 in. 2 AVc 13.78 = =1 AVco 13.78
Fig. RD.6.2.1(a)
ψ ed,V = 1.0 since ca 2 > 1.5ca 1
Eq. (D-27)
ψ c,V = 1.4 for uncracked concrete
D.6.2.7
2
2
ANao = (s cr,Na ) = (12.92) = 166.93"
2
c cr,Na
Eq. (D-16c)
6.46
ψp,Na = max [c a,min ; c cr,Na ] when c a,min < c ac c ac
Eq. (D-16p)
ψp,Na = max [1.75; 6.46] = 6.46 = 0.48 13.5 13.5 φ = 0.65 for dry concrete
This catalog
Calculating for φN a : φN a = 0.65x 106.07 x0.78x0.48x17,120 = 2,647 lb. > 900 lb. – OK 166.93 6. Check all failure modes under tension loading:
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Eq. (D-2)
substituting: φV cb = φ AVc ψ ed,V ψ c,V 7 e AVco d o
2,422 = 12.92" ≤ 3h = 13.5" ef 1,450
s cr,Na = 12.92" s 12.92 c cr,Na = cr,Na = = 6.46" 2 2
φV cb ≥ V ua
D.4.1.2
Summary: Steel capacity = 13,313 lb. Concrete breakout capacity = 2,004 lb. ← Controls Adhesive capacity = 2,647 lb. ∴ φN n = 2,004 lb. as concrete breakout capacity controls
D.6.2.1
d o = 0.5 in. e = 8d 0 = 8 (0.5) = 4"
D.6.2.2
ca 1 = 1.75 in.
φV cb = 0.70 x 1 x 1.0 x 1.4 x 7 x
( 0.54 )
0.2
x √0.5
x √3,000 x (1.75) 1.5 = 932 lb. > 680 lb. – OK 9. Concrete pryout capacity per AC308 V cp = min[k cp N a ; k cp N cb ]
Eq. (D-30a)
D.6.1
φV sa ≥ V ua
k cp = 2.0 for h ef ≥ 2.5"
Eq. (D-2)
N a = 4,072 lb. from adhesive-capacity calculation without φ factor
V sa = 10,650 lb.
This catalog
7. Steel capacity under shear loading:
φ = 0.65
Calculating for φV sa :
φV sa = 0.65 x 10,650 = 6,923 lb. > 680 lb. – OK
This catalog
N cb = 3,083 lb. from concrete-breakout calculation without φ factor V cp = (2.0)(3,083) = 6,166 lb. controls
φ = 0.7
This catalog
φV cp = (0.7)(6,166) = 4,316 lb. > 680 lb. – OK
Continued on next page.
27
EXAMPLE CALCULATION Adhesive Anchors (ICC-ES AC308) Continued from previous page. CALCULATIONS AND DISCUSSION
REFERENCE
10. Check all failure modes under shear loading:
D.4.1.2
Summary: Steel capacity
= 6,923 lb.
Concrete breakout capacity = 932 lb. ← Controls Pryout capacity
= 4,316 lb.
∴ φV n = 932 lb. as concrete breakout capacity controls
11. Check interaction of tension and shear forces: If 0.2 φV n ≥ V ua, then the full tension design strength is permitted.
D.7 D.7.1
By observation, this is not the case. If 0.2 φN n ≥ N ua , then the full shear design strength is permitted
D.7.2
By observation, this is not the case. Therefore: N ua V + ua ≤ 1.2 φN n φV n
Eq. (D-31)
900 680 + = 0.45 + 0.73 = 1.18 < 1.2 – OK 2,004 932
12. Summary
A single ¹⁄₂" diameter ASTM A193 Grade B7 anchor rod in SET-XP epoxy adhesive at a 4 ¹⁄₂" embedment depth is adequate to resist the applied service tension and shear loads of 560 lb. and 425 lb., respectively. ™
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28
EXAMPLE CALCULATION Torque Controlled Adhesive Anchors (ICC-ES AC308) Example calculation for a single IXP™ anchor with SET-XP™ epoxy using USD: Determine if a single ¹⁄₂" diameter IXP™ torque-controlled adhesive anchor with SET-XP™ epoxy with a minimum 4 ⁷⁄₈" embedment (h ef = 4⁷⁄₈") installed 4⁷⁄₈" from the edge of a 12" deep spandrel beam is adequate for a service tension load of 2,500 lb. for wind and a reversible service shear load of 450 lb. for wind. The anchor will be in the tension zone, away from other anchors in ƒ'c = 3,000 psi normal-weight concrete. The anchor will be subjected to a maximum short-term temperature of 180 ˚F and a maximum long-term temperature of 75 ˚F. Continuous inspection will be provided.
2,500 lb. 450 lb. 4⁷⁄₈"
4⁷⁄₈"
Reference the appropriate tables in this catalog for IXP anchor with SET-XP epoxy performance values as determined from test ing in accordance with ICC-ES AC308.
CALCULATIONS AND DISCUSSION
REFERENCE
Note: Calculations are performed in accordance with ICC-ES AC308 and ACI 318-05. 1. Determine the factored tension and shear design loads:
Note: Rebar not shown for clarity.
CALCULATIONS AND DISCUSSION
REFERENCE
4. Concrete breakout capacity under tension loading:
D.5.2
φN cb ≥ N ua ACI 318, 9.2.1 N cb =
N ua = 1.6W = 1.6 x 2,500 = 4,000 lb. V ua = 1.6W = 1.6 x 450 = 720 lb.
Eq. (D-1)
ANc ψ ψ ψ ed,N c,N cp,N N b ANco
where: N b = k c √ƒ 'c h ef 1.5
2. Design considerations:
D.4.1.2
This is a combined tension and shear interaction problem where values for both φN n and φV n need to be determined. φN n is the lesser of the design tension strength controlled by: steel ( φN sa ), concrete breakout (φN cb ), or pull-out ( φnN pn ). φV n is the lesser of the design shear strength controlled by: steel ( φV sa ), concrete breakout (φV cb ), or pryout ( φV cp ).
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3. Steel capacity under tension loading:
Eq. (D-4);
Eq. (D-7)
substituting:
φN cb = φ ANc ψ ed,N ψ c,N ψ cp,N k c √ƒ 'c h ef 1.5 ANco
where:
D.5.1
φN sa ≥ N ua
Eq. (D-1) .
N sa = 11,075 lb.
This catalog
φ = 0.75
This catalog
n = 1 (single anchor) Calculating for φN sa :
φN sa = 0.75 x 1 x 11,075 = 8,306 lb. > 4,000 lb. – OK ∴ ¹⁄₂ in. diameter anchor is adequate
k c = k cr = 17 (Anchor is installed in a tension zone, therefore, cracking is assumed at service loads)
This catalog
ψ cp,N = 1.0
D.5.2.7
ψ = 0.7 + 0.3 c a,min when c ed,N a,min < 1.5 h ef 1.5h ef
Eq. (D-11)
by observation, c a,min = 4⁷⁄₈ < 1.5h ef
ψ ed,N = 0.7 + 0.3
(4⁷⁄₈) 1.5(4⁷⁄₈)
= 0.90
ψ c,N = 1.0 assuming cracking at service loads (ft > fr)
D.5.2.6
φ = 0.65 for Condition B
This catalog
(no supplementary reinforcement provided) ANco = 9h ef 2 = 9(4 ⁷⁄₈)2 = 213.89 in. 2
Eq. (D-6)
ANc = (ca 1 + 1.5h ef )(2 x 1.5h ef ) = (4⁷⁄₈ + 1.5(4 ⁷⁄₈))(2 x 1.5(4 ⁷⁄₈)) = 178.24 in. 2
Fig. RD.5.2.1(a)
ANc 178.24 = = 0.83 ANco 213.89 Calculating for φN cb : Would you like help with these c alculations? Visit www.simpsonanchors.com to download the Simpson Strong-Tie ® Anchor Designer ™ software.
φN cb = 0.65 x 0.83 x 1.0 x 0.90 x 1.0 x 17 x √3,000 x (4 ⁷⁄₈)1.5 = 4,866 lb. > 4,000 lb. – OK
Continued on next page.
29
EXAMPLE CALCULATION Torque Controlled Adhesive Anchors (ICC-ES AC308) Continued from previous page. CALCULATIONS AND DISCUSSION
REFERENCE
5. Pullout capacity:
D.5.3
Pullout capacity, N pn,cr , is established by reference tests in cracked concrete by the reliability test of AC 308. Pullout capacity does not need to be calculated for IXP with SET-XP epoxy since steel failure controls over pullout capacity. ™
™
6. Check all failure modes under tension loading: Summary: Steel capacity
D.4.1.2
= 8,306 lb.
Concrete breakout capacity = 4,866 lb. ← Controls Pullout capacity = N/A ∴ φN n = 4,866 lb. as concrete breakout capacity controls 7. Steel capacity under shear loading:
D.6.1
REFERENCE
9. Concrete pryout strength:
D.6.3
φnV cp ≥ V ua
Eq. (D-2)
V cp = k cp N cb
Eq. (D-29)
where: n = 1 k cp = 2.0 and φ = 0.70 4,866 = 14,972 lb. k cp N cb = 2.0 x 0.65
This catalog D.6.3.1
φnV cp = 0.70 x 1 x 14,972 = 10,480 lb. > 720 lb.
–
OK
10. Check all failure modes under shear loading:
D.4.1.2
φV sa ≥ V ua
Eq. (D-2)
Summary:
V sa = 10,450 lb.
This catalog
Steel capacity
This catalog
Concrete breakout capacity = 3,096 lb. ← Controls
φ = 0.65
Calculating for φV sa :
φV sa = 0.65 x 10,450 = 6,793 lb. > 720 lb.
–
Pryout Capacity
OK
8. Concrete breakout capacity under shear loading:
Eq. (D-2)
AVc ψ ψ ed,V c,V V b AVco
Eq. (D-21)
(d o e )
0.2
√d o √ƒ 'c c a11.5
Eq. (D-24)
substituting: φV cb = φ AVc ψ ed,V ψ c,V 7 e AVco d o
If 0.2 φV n ≥ V ua, then the full tension design strength is permitted.
D.7 D.7.1
If 0.2 φN n ≥ N ua , then the full shear design strength is permitted
D.7.2
By observation, this is not the case.
( )
0.2
√d o √ƒ 'c c a11.5
Therefore:
where:
N ua V + ua ≤ 1.2 φN n φV n
φ = 0.70 for Condition B (no supplementary reinforcement provided)
D4.4(c)(i)
2
AVco = 4.5ca 1
= 4.5(4 ⁷⁄₈)
11. Check interaction of tension and shear forces:
By observation, this is not the case.
where: V b = 7
= 10,480 lb.
D.6.2
φV cb ≥ V ua V cb =
= 6,793 lb.
∴ φV n = 3,096 lb. as concrete breakout capacity controls
∴ ¹⁄₂ in. diameter anchor is adequate
Eq. (D-23)
4,000 720 + = 0.82 + 0.23 = 1.05 < 1.2 4,866 3,096
Eq. (D-31)
–
OK
2
∴ AVco = 106.95 in. 2
12. Summary
AVc = 2(1.5c a 1)(1.5ca 1)
Fig. RD.6.2.1(a)
= 2(1.5(4 ⁷⁄₈))(1.5(4⁷⁄₈))
∴ AVc = 106.95 in. 2 AVc = 106.95 = 1 AVco 106.95
D.6.2.1
ψ ed,V = 1.0 since c a 2 > 1.5ca 1
Eq. (D-27)
ψ c,V = 1.0 assuming cracking at service loads (ft > fr)
D.6.2.7
d o = 0.5 in. e = 8d 0 = 8 (0.5) = 4"
D.6.2.2
ca 1 = 4⁷⁄₈ in.
φV cb = 0.70 x 1 x 1.0 x 1.0 x 7 x 30
CALCULATIONS AND DISCUSSION
( 0.54 )
0.2
x √0.5
x √3,000 x (4 ⁷⁄₈)1.5 = 3,096 lb. > 720 lb.
–
OK
A single ¹⁄₂" diameter IXP anchor with SET-XP epoxy at a 4 ⁷⁄₈" embedment depth is adequate to resist the applied service tension and shear loads of 2,500 lb. and 450 lb., respectively.
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