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"EMBEDPL" --- Embedment Strength of stud plate Demo Version Program Description: "EMBEDPL.xls" is a MS-Excel spreadsheet workbook for the analysis of a (4) Headed Concrete Anchors, HCA, and (2) HCAs, per ACI 318-08, Appendix D. The spreadsheet is designed to find the embedment strength in concrete for the required plate within certain concrete parameters. The spreadsheet is protected.
Program Environment:
Microsoft Office Excel 2003
Creation Date:
May 29th, 2009
Design References:
1. ACI 318-08 2. PCI Design Handbook, 6th Edition
This program is a workbook consisting of three (3) worksheets, described as follows: Worksheet Name
Description
DOC
This documentation sheet
EMBEDPL
Embedment Strength of (4) stud plate
EMBEDPL (2)
Embedment Strength of (2) stud plate
REVISION 1.4: (8/30/2013) Fixed glitch on eccentricity with and without tension. Program Assumptions and Limitations: 1. This spreadsheet program is intended to analyze and design the embedment of four headed concrete anchors affixed to a rigid plate. Shear and tension embedment strength is calculated per Appendix D of ACI 318. The bearing capacity is calculated per Section 10 & 11 of ACI 318. 2. This program assumes that the anchor strength is not governed by ductile yielding of the anchored steel which would cause significant redistribution of anchor forces and that the attachment that distributes the loads to the anchors is sufficiently stiff. 3. The required strength is calculated from the applicable load combinations in Section 9.2. 4. This spreadsheet, as well as the provisions of Appendix D, do not apply to the design of anchors in hinge zones of concrete structures under seismic loads. 5. This program assumes that the studs are not post-tensioned, post-installed, or torqued controlled anchors. However for conservative calculations, the minimum edge distance required uses limitation for torque controlled anchors (actual minimum edge distance per section 7.7) 6. This program assumes that the member clear cover is 2 inches for the purpose of punching shear calculations. 7. This program does not afford entry of eccentricity in the z-axis. 8. This program does not for strength of the plate itself or the welding affixing the studs to the plate. 9. This program contains numerous “comment boxes” which contain a wide variety of information including explanations of input or output items, equations used, data tables, etc. (Note: presence of a “comment box” is denoted by a “red triangle” in the upper right-hand corner of a cell. Merely move the mouse pointer to the
desired cell to view the contents of that particular "comment box".)
Program Theory and Operation: The top left of the spreadsheet screen allows for input of required information in lightly yellow highlighted boxes. Information required includes the following:
Anchorage Spreadsheet: Input: 1. Loads: a. Nua (Ultimate Factored Tensile Load) in kips b. Vua (Ultimate Factored Shear Load) in kips in the x direction c. Vua (Ultimate Factored Shear Load) in kips in the y direction d. ex, Eccentricity of load about the x-axis d. ey, Eccentricity of load about the y-axis 2. Dimensions: a. bx1, Steel edge distance: distance from the centerline of bolt to the edge of plate in x direction. b. bx2, Steel edge distance: distance from the centerline of bolt to the edge of plate in x direction. c. by1, Steel edge distance: distance from the centerline of bolt to the edge of plate in y direction. d. by2, Steel edge distance: distance from the centerline of bolt to the edge of plate in y direction. e. sx1, Stud spacing distance: distance between the centerline of bolts in x direction. f. sy1, Stud spacing distance: distance between the centerline of bolts in y direction. [only in "EMBEDPL"] g. cx1, Concrete edge distance: distance from the centerline of bolt to the edge in x direction. h. cx2, Concrete edge distance: distance from the centerline of bolt to the edge in x direction. i. cy1, Concrete edge distance: distance from the centerline of bolt to the edge in y direction. j. cy2, Concrete edge distance: distance from the centerline of bolt to the edge in y direction. 3. Parameters : a. Stud Anchor Diameter, db b. Specified Compressive strength of Concrete, f'c c. Specified Yield strength of anchor steel, fy d. Specified Tensile strength of anchor steel, futa e. Steel element, Ductile or Brittle: per Section D.1 f. The overall depth through which the anchor transfers force to and from the concrete, hef g. Thickness of member in which an anchor is located, ha h. Potential Failure Surfaces crossed by supplementary reinforcement (Section D.4.2.1) i. Is there anticipation of cracking at service levels (See Section D.6.2.7)? j. Are anchors are located in structure assigned to Seismic Design Category C, D, E, or F. (Sect. D3.3)? k. Concrete Type per Section 2.2. l. Per Section D.6.2.3? For cast-in headed studs that are continuously welded to steel attachments having a minimum thickness of > 3/8" and db/2 provided that: (a) spacing > 2.5 in. and (b) reinforcement is provided at the corners if ca2 < 1.5hef.
Output: 1. Steel strength of anchor in tension: (SEC D.5.1)
Nsa =
nAse,Vfuta
2. Concrete Breakout strength of anchor in tension: (SEC D.5.2)
Ncb =
Anc
Yed,NYc,NY,NNb
Single Anchor
Yec,NYed,NYc,NY,NNb
Group of Anchors
Anco Ncbg =
Anc Anco
3. Pullout strength of anchor in tension: (SEC D.5.3)
Npn =
Yc,PNp
Np =
Abrg8f'c
Single Anchor
4. Concrete Side-Face Blowout strength of Headed anchor in tension: (SEC D.5.4)
Nsb =
160ca1Abrg1/2f'c1/2
For cast-in headed stud anchors
5. Steel strength of anchor in shear: (SEC D.6.1)
Vsa =
nAse,Vfuta
6. Concrete Breakout strength of anchor in shear: (SEC D.6.2)
Vcb =
Avc
Single Anchor
Avco Group of Anchors
Vcb =
Av
Yec,V Yed,VYc,VYh,VVb
Avco 7. Concrete Pryout strength of anchor in shear: (SEC D.6.3)
V =
kNcb
Vg =
kNcbg
8. Interaction of tensile and shear forces: (SEC D.7)
if Vua < 0.2fVn
fNn > NUA
if Nua < 0.2fNn
fVn > VUA
if Nua > 0.2fNn & Vua > 0.2fVn
NUA ΦNn
9. Required edge distances & spacings: (ACI 318-08 Section D.7 & ASIC Table J3.4)
See Calculated section 10. Plate Bearing: (ACI 318-08 Section 10.14)
A1 = (bx1 + cx1 + bx2)(by1 + sy1 + by2) A2 = (cx1 + cx1 + cx2)(cy1 + sy1 +cy2) Multiplication Factor = (A2/A1)^0.5 < 2.0 ΦPn = Φ0.85fc'A1 x (Multiplication Factor) 11. Plate Punching Shear: (ACI 318-08 Section 11.12.2.1)
bo = (bx1 + cx1 + bx2) + (by1 + sy1 + by2) d = ha - 2in. (Assume 2" clear cover) b = Length of: Long side of plate / Short side of plate Factor = Minimum of (2 + 4/b) or 4 Vc = Factor x (fc')^0.5 x bo x d
+
VUA ΦVn
<
1.2
EMBEDMENT PLATE CALCULATION (Demo Version)
Job Name: Job Number:
Per Building Code Requirements for Structural Concrete (ACI 318-08) Design of (4) Stud Embed Plate Anchorage per Appendix D Subject: Date: Originator: Checker:
Input Data: Loads: Nua =
9
kips
Vua,x =
0
kips
Vua,y =
2 1 1.5
kips
ex = ey =
(Tension)
in. in.
Dimensions: bx1 = bx2 =
2 2
in.
PL Edge Distance
in.
PL Edge Distance
by1 =
2
in.
PL Edge Distance
by2 =
2
in.
PL Edge Distance
sx1 = sy1 = cx1 = cx2 = cy1 = cy2 =
4 4 48 48 4 12
in.
Spacing in x-dir.
in.
Spacing in y-dir.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
#1: #2:
Parameters: Anchor Dia., db = Concrete, f'c=
#3:
Stud Reactions (k) Axial Rz Shear Rh 0.56 0.40 -1.69 0.64 -2.81 0.40 -5.06 0.64
1/2 3000
in.
Stud Anchor Diameter
psi
Specified Compressive strength of Concrete
Anchor, fy =
51
ksi
Specified Yield strength of anchor steel
Anchor, futa =
65
ksi
Specified Tensile strength of anchor steel
Steel Element = Embedment, hef = Thickness, ha = Supp. Reinf.? Cracking Anticip.? Seismic (Chapt.21) Concrete Type = Per Sect. D.6.2.3?
Ductile
#4:
(Section D.1)
4
in.
The overall depth through which the anchor transfers force to and from the concrete.
6 Yes No No
in.
Thickness of member in which an anchor is located,
Normalwt Yes
Potential Failure Surfaces crossed by supplementary reinforcement (Section D.4.2.1) Cracking at service levels (Section D.6.2.7
Case?
Case 2
Anchors are located in structure assigned to Seismic Design Category C, D, E, or F. (Sect. D3.3) (Section 2.2) For cast-in headed studs that are continuously welded to steel attachments having a minimum thickness of > 3/8" and db/2 provided that: (a) spacing > 2.5 in. and (b) reinforcement is provided at the corners if ca2 < 1.5hef.
Results: 1. Steel strength of anchor in tension: (Section D.5.1) Nsa =Asefuta (Equation D-3)
Ase, N =
0.2
in2
Nsa =
13.00
kips
ΦNsa =
9.75
kips / bolt
Effective Cross Sectional Area of Anchor
Φ= Nu,max =
5.06
kips
=>
OK
2. Concrete Breakout strength of anchor in tension: (Section D.5.2) Ncbg = Anc Yec,NYed,NYc,NY,NNb (Equation D-5) Anco Anc =
224.00
in2
Anco =
144.00
in2
Yec,N(x-dir) =
Anco = 9hef2 Yec,N =
0.87
1
<1
Yec,N(y-dir) =
0.92
Yec,N(comb.) =
0.80
Yed,N =
0.90
e'Nx
=
1.29
in
Eccentricity of all tension forces on a group of anchors in the x dir.
e'Ny
=
0.82
in
Eccentricity of all tension forces on a group of anchors in the y dir.
Yc,N =
1.25
Yc,N = 1.25 for Cast-in-place anchors
Y,N =
1 1
Y,N = 1.0 for Cast-in-place anchors
l= kc = Nb =
24 10.52
(1 + 2e'N 3hef Yed,N = 1 (if Cmin > 1.5hef ) -OR-
kips
) 0.7 + 0.3cmin / (1.5 hef)
kc = 24 for Cast-in-place anchors Nb = klf'c1/2hef3/2 Nb,max = 16lf'c1/2hef5/3 if 11in. < hef < 25in. Φ=
ΦNcbg =
11.06
Nua =
kips
3. Pullout strength of anchor in tension: (Section D.5.3) Npn =Yc,PNp Abrg =
0.59
Np =
14.16
Yc,P=
1.40
ΦNpn =
14.87
9.00
kips
=>
OK
(Equation D-14)
in2
Np =Abrg8f'c
(Equation D-15)
Φ= kips / bolt
Nu,max =
5.06
kips
=>
OK
4. Concrete Side-Face Blowout strength of Headed anchor in tension: (Section D.5.4) Nsb = 160ca1Abrg1/2lf'c1/2 (Equation D-17) Nsbg = (1 + s/6ca1)Nsb
(Equation D-18)
Ca1 =
4.00
Ca2 =
48.00
Ca2 / Ca1 =
3.00
Factor = Nsb =
1.00 N/A
kips
Ca1 > 0.4 hef => Not Applicable (Section D.5.4.1)
Nsbg =
N/A
kips
Ca1 > 0.4 hef and/or s > 6ca1=> Not Applicable (Section D.5.4.2)
ΦN =
N/A
kips
1.0 < Ca2 / Ca1 < 3.0
Nu,max =
1.69
kips
=>
Φ=
N/A
5. Steel strength of anchor in shear: (Section D.6.1) Vsa =Ase,Vfuta Ase,V =
0.20
in2
futa =
65.00
ksi
Vsa =
13.00
kips/bolt
ΦVsa =
8.45
kips/bolt
(Equation D-19)
Effective Cross Sectional Area of Anchor
Φ= Vu,max =
0.64
kips
=>
OK
6. Concrete Breakout strength of anchor in shear: (Section D.6.2)* Vb = 8 (le/da)0.2da1/2lf'c1/2Ca11.5 Vcbg =
(Equation D-25)
Yec,VYed,VYc,VYh,VVb
Avc
(Equation D-22)
Avco ha =
6.00
in
Thickness of member in which an anchor is located
le =
4.00
in
Load bearing length (le = minimum of hef or8 da))
da =
0.50
in
da = db (Outside diameter of shaft of headed stud)
e'vx
=
1.00
in
Eccentricity of shear force on a group of anchors in the x dir.
e'vy
=
1.50
in
Eccentricity of shear force on a group of anchors in the y dir.
l= Yc,V=
1
Yed,V=
N/A
Yed,V = 1 (if ca2 > 1.5ca1) or 0.7 + 0.3ca2/(1.5ca1)
Yh,V=
N/A
Yh,V = (1.5ca1/ha)^0.5 < 1.0
AVC =
N/A
in2
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1,sy1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*ca1,ha)
AVCO =
N/A
in2
AVCO = 4.5(ca1)^2
Vb =
N/A
kips
Vcbg,x =
N/A
kips
ΦVcbg,x =
N/A
kips
Concrete Type Modification Factor
1.40 Cracking Modification Factor (per Section D.6.2.7) X - Direction (perpendicular to edge): N/A ca1 = in ca1 = (cx1 or cx2) + sx1 or minimum required per Section D.6.2.4 Yec,V= Yec,V = 1 / (1+2e'v,y/(3ca1)) N/A
Φ= Vu,max =
N/A
kips
=>
N/A
Y - Direction (perpendicular to edge): ca1 =
16.00
in
ca1 = (cy1 or cy2) + sy1 or minimum required per Section D.6.2.4
Yec,V=
0.96
Yec,V = 1 / (1+2e'v,y/(3ca1))
Yed,V=
1.00
Yed,V = 1 (if ca2 > 1.5ca1) or 0.7 + 0.3ca2/(1.5ca1)
Yh,V=
1.00
Yh,V = (1.5ca1/ha)^0.5 < 1.0
AVC =
312.00
in2
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1,sy1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*ca1,ha)
AVCO =
1152.00
in2
AVCO = 4.5(ca1)^2
Vb =
30.06
kips
Vcbg,y =
10.94
kips
ΦVcbg,y =
8.21
kips
X - Direction (parallel to edge): Vcbg,x = 12.02 kips ΦVcbg,x =
9.02 kips Y - Direction (parallel to edge): Vcbg,y = 8.82 kips
0.2 1/2 1/2 1.5 Vb = 8 (le/da) da lf'c Ca1
Φ= Vu,max =
2.00
kips
=>
OK Φ=
Per Section D.6.2.1.(c)
Vu,max =
N/A
kips
=>
N/A Φ=
Per Section D.6.2.1.(c)
Vu,max = OK 6.61 2.00 kips => kips *NOTE: Case 1 calculation (evaluation of bolt to closest edge) not req'd. (See Section RD6.2.1, 3rd paragraph) ΦVcbg,y =
7. Concrete Pryout strength of anchor in shear: (Section D.6.3) Vg =kNcbg
(Equation D-31)
k =
2.00
Ncbg =
14.74
kips
Vg =
29.48
kips
ΦVg =
22.11
kips
k = 1.0 (for hef < 2.5in.); k = 2.0 (for hef > 2.5in.) from Equation D-5 (See previous Section D.5.2 calcs)
Φ= Vu,max =
2.07
kips
=>
Vu,max = sum of each bolt shear
OK
8. Interaction of tensile and shear forces: (Section D.7)
NUA
Tension Ratio =
ΦNn Steel: Breakout: Pullout: Sideface Blowout:
0.519 0.814 0.340 N/A
Steel strength of anchor in tension Concrete Breakout strength of anchor in tension Pullout strength of anchor in tension Concrete Side-Face Blowout strength of Headed anchor in tension
VUA
Shear Ratio =
ΦVn Steel: Breakout (Case2): Breakout (Case3): Pryout:
NUA
Combined Stress Ratio (CSR) =
ΦNn CSR:
0.075 0.244 0.302 0.093
+
Steel strength of anchor in shear Concrete Breakout strength of anchor in shear - perp. Concrete Breakout strength of anchor in shear - parallel Concrete Pryout strength of anchor in shear
VUA ΦVn
<
1.2
1.12
OK
EMBEDMENT STRENGTH (Per ACI 318-08 - Appendix D) 9. Required edge distances & spacings: (ACI 318-08 Section D.7 & ASIC Table J3.4) smin =
2.00
in
Minimum spacing =
sact =
4.00 3.00
in
Actual lesser of two spacings, sy1 & sx1
in
Assume torqued cast-in headed anchors (conservative). See Section 7.7 else.
4.00 0.88
in
Actual lesser of four edge distances, cy1/2 & cx1/2
in
Minimum steel edge distance per Table J3.4
in
Actual lesser of four edge distances, cy1/2 & cx1/2
Req'd thick., ha,min =
2.00 4.75
in.
ha,min = hef + 0.75"
Actual thickness, ha =
6.00
in.
Conc. Edge dist, min = Conc. Edge dist, act = Edge dist, min = Edge dist, act =
smin = 4 x da (for untorqued cast-in-place anchors)
OK OK OK OK
10. Plate Bearing: (ACI 318-08 Section 10.14) 64.00 in2 Plate Area, A1 = A1 = (bx1 + sx1 + bx2)(by1 + sy1 + by2) 2 Concrete Area, A2 = 2000.00 in A2 = (cx1 + sx1 + cx2)(cy1 + sy1 +cy2) 2.00 Multiplication Factor = Multiplication Factor = (A2/A1)^0.5 < 2.0 326.40 kips Pn = Pn = 0.85fc'A1 x (Multiplication Factor) ΦPn =
212.16
kips
Nua =
N/A
kips
=>
11. Plate Punching Shear: (ACI 318-08 Section 11.12.2.1) 16.00 Perimeter, bo = in bo = (bx1 + sx1 + bx2) + (by1 + sy1 + by2) 4.00 Concrete depth, d = in d = ha - 2in. (Assume 2" clear cover) 1.00 b= b = Length of: Long side of plate / Short side of plate
N/A
Factor = Vc = ΦVc =
4.00 14.02
kips
9.11
kips
Factor = Minimum of (2 + 4/b) or 4 Vc = Factor x (fc')^0.5 x bo x d
Nua =
N/A
kips
=>
N/A
on)
18-08) D 11/9/2017 19:16
Xo (in.) Bolt#1 Bolt#2 Bolt#3 Bolt#4 Bolt Dist. to X,Y axis: Bolt No.: ### ### ### ### Bolt Group Properties: S Xo = S Yo = Xc = Yc = S Ix = S Iy = J= S Ixy = q= S Pz = S Px = S Py = S Mx =
e to and from the concrete.
S My = S Mz =
forcement (Section D.4.2.1)
###
APPENDIX D:
C, D, E, or F. (Sect. D3.3)
###
Steel f Factor Selection:
ents having a minimum
einforcement is provided
Tension Ductile Brittle
Concrete f Factor Selection: Condition A Shear Loads
Cast-in:
0.75 (continued)
2. Section D.5.2: Anc,max = Edges = hef =
4. Section D.5.4: ca1 = ca2 = ca2 / ca1= Factor = Single or Group? (if Cmin < 1.5hef)
Nu,max =
sx1 = sy1 = cx1 = cx2 = cy1 =
0.75 Yc,V= CASE 1:
CASE 2:
CASE 3:
0.75 CASE 2:
Vu(-)x = Yec,V= Yed,V= Yh,V= ca1 = ca2(a) = ca2(b) =
AVC = AVCO = 0.75 Vcbg,x =
Influence Edges? CASE 2:
Vu(+)x = Yec,V= Yed,V= Yh,V= 0.65 ca2(a) = (continued)
AVC = AVCO = Vb = Vcbg,x = Influence Edges? CASE 2:
Vu(+)y = Yec,V= Yed,V= Yh,V= ca1 = ca2(a) = ca2(b) =
AVC = AVCO = Vb =
a2(b))) x MIN(1.5*ca1,ha)
Vcbg,y = Vcbg,x =
0.75 CASE 2:
Vu(+)y = Yec,V= Yed,V= Yh,V= ca1 =
a2(b))) x MIN(1.5*ca1,ha)
ca2(a) = ca2(b) =
AVC = 0.75 Vb = Vcbg,y = 0.75
0.75
6.2.1, 3rd paragraph)
0.75
(continued)
f anchor in tension
strength of Headed anchor
f anchor in shear - perp.
f anchor in shear - parallel
nchor in shear
See Section 7.7 else.
EMBEDMENT PLATE CALCULATION (Demo Version)
Job Name: Job Number:
Per Building Code Requirements for Structural Concrete (ACI 318-08) Design of (2) Stud Embed Plate Anchorage per Appendix D Subject: Date: Originator: Checker:
Input Data: Loads: Nua =
6.5
kips
Vua,x =
1
kips
Vua,y =
kips
ex = ey =
5 1 0
Dimensions: bx1 = bx2 =
2 2
in.
PL Edge Distance
in.
PL Edge Distance
by1 =
2
in.
PL Edge Distance
by2 =
2
in.
PL Edge Distance
sx1 = cx1 = cx2 = cy1 = cy2 =
4 48 48 12 44
in.
Spacing in x-dir.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
(Tension)
in. in.
#1:
Parameters: Anchor Dia., db = Concrete, f'c= Anchor, fy = Anchor, futa = Steel Element =
#2:
Stud Reactions (k) Axial Rz Shear Rh -1.62 1.35 -4.88 3.78
1/2 3000 51
in.
Stud Anchor Diameter
psi
Specified Compressive strength of Concrete
ksi
Specified Yield strength of anchor steel
65
ksi
Specified Tensile strength of anchor steel
Ductile
(Section D.1)
Embedment, hef = Thickness, ha =
4
in.
The overall depth through which the anchor transfers force to and from the concrete.
6
in.
Thickness of member in which an anchor is located,
Supp. Reinf.? Cracking Anticip.? Seismic (Chapt.21) Concrete Type = Per Sect. D.6.2.3?
No No No Normalwt No
Potential Failure Surfaces crossed by supplementary reinforcement (Section D.4.2.1) Cracking at service levels (Section D.6.2.7)
Case?
Case 3
Anchors are located in structure assigned to Seismic Design Category C, D, E, or F. (Sect. D3.3) (Section 2.2) For cast-in headed studs that are continuously welded to steel attachments having a minimum thickness of > 3/8" and db/2 provided that: (a) spacing > 2.5 in. and (b) reinforcement is provided at the corners if ca2 < 1.5hef.
Results: 1. Steel strength of anchor in tension: (Section D.5.1) Nsa =Asefuta (Equation D-3)
Ase, N =
0.2
in2
Nsa =
13.00
kips
ΦNsa =
9.75
kips / bolt
Effective Cross Sectional Area of Anchor
Φ= Nu,max =
4.88
kips
=>
OK
2. Concrete Breakout strength of anchor in tension: (Section D.5.2) Ncbg = Anc Yec,NYed,NYc,NY,NNb (Equation D-5) Anco Anc =
192.00
in2
Anco =
144.00
in2
Yec,N(x-dir) =
Anco = 9hef2 Yec,N =
0.90
1
<1
Yec,N(y-dir) =
1.00
Yec,N(comb.) =
0.90
Yed,N =
1.00
e'Nx
=
1.00
in
Eccentricity of all tension forces on a group of anchors in the x dir.
e'Ny
=
0.00
in
Eccentricity of all tension forces on a group of anchors in the y dir.
Yc,N =
1.25
Yc,N = 1.25 for Cast-in-place anchors
Y,N =
1 1
Y,N = 1.0 for Cast-in-place anchors
l= kc = Nb =
24 10.52
(1 + 2e'N 3hef Yed,N = 1 (if Cmin > 1.5hef ) -OR-
kips
) 0.7 + 0.3cmin / (1.5 hef)
kc = 24 for Cast-in-place anchors Nb = klf'c1/2hef3/2 Nb,max = 16lf'c1/2hef5/3 if 11in. < hef < 25in. Φ=
ΦNcbg =
11.04
Nua =
kips
3. Pullout strength of anchor in tension: (Section D.5.3) Npn =Yc,PNp Abrg =
0.59
Np =
14.16
Yc,P=
1.40
ΦNpn =
13.88
6.50
kips
=>
OK
(Equation D-14)
in2
Np =Abrg8f'c
(Equation D-15)
Φ= kips
Nu,max =
4.88
kips
=>
OK
4. Concrete Side-Face Blowout strength of Headed anchor in tension: (Section D.5.4) Nsb = 160ca1Abrg1/2lf'c1/2 (Equation D-17) Nsbg = (1 + s/6ca1)Nsb
(Equation D-18)
Ca1 =
12.00
Ca2 =
48.00
Ca2 / Ca1 =
3.00
Factor = Nsb =
1.00 N/A
kips
Ca1 > 0.4 hef => Not Applicable (Section D.5.4.1)
Nsbg =
N/A
kips
Ca1 > 0.4 hef and/or s > 6ca1=> Not Applicable (Section D.5.4.2)
ΦN =
N/A
kips
1.0 < Ca2 / Ca1 < 3.0
Nu,max =
4.88
kips
=>
Φ=
N/A
5. Steel strength of anchor in shear: (Section D.6.1) Vsa =Ase,Vfuta Ase,V =
0.20
in2
futa =
65.00
ksi
Vsa =
13.00
kips/bolt
ΦVsa =
8.45
kips/bolt
(Equation D-19)
Effective Cross Sectional Area of Anchor
Φ= Vu,max =
3.78
kips
=>
OK
6. Concrete Breakout strength of anchor in shear: (Section D.6.2)* Vb = 7 (le/da)0.2da1/2lf'c1/2Ca11.5 Vcbg =
Yec,VYed,VYc,VYh,VVb
Avc
(Equation D-24) (Equation D-22)
Avco ha =
6.00
in
Thickness of member in which an anchor is located
le =
4.00
in
Load bearing length (le = minimum of hef or8 da))
da =
0.50
in
da = db (Outside diameter of shaft of headed stud)
e'vx
=
1.00
in
Eccentricity of shear force on a group of anchors in the x dir.
e'vy
=
0.00
in
Eccentricity of shear force on a group of anchors in the y dir.
l= Yc,V=
1
Yed,V=
0.77
Yed,V = 1 (if ca2 > 1.5ca1) or 0.7 + 0.3ca2/(1.5ca1)
Yh,V=
1.00
Yh,V = (1.5ca1/ha)^0.5 < 1.0
AVC =
336.00
in2
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*ca1,ha)
AVCO =
5000.00
in2
AVCO = 4.5(ca1)^2
Vb =
79.08
kips
Vcbg,x =
5.74
kips
ΦVcbg,x =
4.02
kips
Concrete Type Modification Factor
1.40 Cracking Modification Factor (per Section D.6.2.7) X - Direction (perpendicular to edge): 33.33 ca1 = in ca1 = (cx1 or cx2) + sx1 or minimum required per Section D.6.2.4 Yec,V= Yec,V = 1 / (1+2e'v,y/(3ca1)) 1.00
Φ= Vu,max =
1.00
kips
=>
OK
Y - Direction (perpendicular to edge): ca1 =
32.00
in
ca1 = (cy1 or cy2) or minimum required per Section D.6.2.4
Yec,V=
0.98
Yec,V = 1 / (1+2e'v,y/(3ca1))
Yed,V=
1.00
Yed,V = 1 (if ca2 > 1.5ca1) or 0.7 + 0.3ca2/(1.5ca1)
Yh,V=
1.00
Yh,V = (1.5ca1/ha)^0.5 < 1.0
AVC =
600.00
AVCO =
4608.00
in2 in
2
Vb =
74.39
kips
Vcbg,y =
13.28
kips
ΦVcbg,y =
9.30
kips
X - Direction (parallel to edge): Vcbg,x = 16.78 kips ΦVcbg,x =
11.75 kips Y - Direction (parallel to edge): Vcbg,y = 12.40 kips
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*ca1,ha) AVCO = 4.5(ca1)^2 0.2 1/2 1/2 1.5 Vb = 7 (le/da) da lf'c Ca1
Φ= Vu,max =
5.00
kips
=>
OK Φ=
Per Section D.6.2.1.(c)
Vu,max =
1.00
kips
=>
OK Φ=
Per Section D.6.2.1.(c)
Vu,max = OK 8.68 5.00 kips => kips *NOTE: Case 1 calculation (evaluation of bolt to closest edge) not req'd. (See Section RD6.2.1, 3rd paragraph) ΦVcbg,y =
7. Concrete Pryout strength of anchor in shear: (Section D.6.3) Vg =kNcbg
(Equation D-31)
k =
2.00
Ncbg =
15.77
kips
Vg =
31.55
kips
ΦVg =
22.08
kips
k = 1.0 (for hef < 2.5in.); k = 2.0 (for hef > 2.5in.) from Equation D-5 (See previous Section D.5.2 calcs)
Φ= Vu,max =
5.13
kips
=>
Vu,max = sum of each bolt shear
OK
8. Interaction of tensile and shear forces: (Section D.7)
NUA
Tension Ratio =
ΦNn Steel: Breakout: Pullout: Sideface Blowout:
0.500 0.589 0.351 N/A
Steel strength of anchor in tension Concrete Breakout strength of anchor in tension Pullout strength of anchor in tension Concrete Side-Face Blowout strength of Headed anchor in tension
VUA
Shear Ratio =
ΦVn Steel: Breakout (Case2): Breakout (Case3): Pryout:
NUA
Combined Stress Ratio (CSR) =
ΦNn CSR:
0.448 0.538 0.576 0.232
+
Steel strength of anchor in shear Concrete Breakout strength of anchor in shear - perp. Concrete Breakout strength of anchor in shear - parallel Concrete Pryout strength of anchor in shear
VUA ΦVn
<
1.2
1.16
OK
EMBEDMENT STRENGTH (Per ACI 318-08 - Appendix D) 9. Required edge distances & spacings: (ACI 318-08 Section D.7 & ASIC Table J3.4) smin =
2.00
in
Minimum spacing =
sact =
4.00 3.00
in
Actual lesser of spacing, sx1
in
Assume torqued cast-in headed anchors (conservative). See Section 7.7 else.
in
Actual lesser of four edge distances, cy1/2 & cx1/2
Edge dist, min =
12.00 0.88
in
Minimum steel edge distance per Table J3.4
Edge dist, act =
2.00
in
Actual lesser of four edge distances, cy1/2 & cx1/2
Req'd thick., ha,min =
4.75
in
ha,min = hef + 0.75"
Actual thickness, ha =
6.00
in
Conc. Edge dist, min = Conc. Edge dist, act =
smin = 4 x da (for untorqued cast-in-place anchors)
OK OK OK OK
10. Plate Bearing: (ACI 318-08 Section 10.14) 32.00 in2 Plate Area, A1 = A1 = (bx1 + sx1 + bx2)(by1 + by2) 2 Concrete Area, A2 = 5600.00 in A2 = (cx1 + sx1 + cx2)(cy1 + cy2) 2.00 Multiplication Factor = Multiplication Factor = (A2/A1)^0.5 < 2.0 163.20 kips Pn = Pn = 0.85fc'A1 x (Multiplication Factor) ΦPn =
106.08
kips
Nua =
N/A
11. Plate Punching Shear: (ACI 318-08 Section 11.12.2.1) 12.00 Perimeter, bo = in bo = (bx1 + sx1 + bx2) + (by1 + by2) 4.00 Concrete depth, d = in d = ha - 2in. (Assume 2" clear cover)
kips
=>
N/A
b= Factor = Vc = ΦVc =
2.00 4.00 10.52
kips
6.84
kips
b = Length of: Long side of plate / Short side of plate Factor = Minimum of (2 + 4/b) or 4 Vc = Factor x (fc')^0.5 x bo x d
Nua =
N/A
kips
=>
N/A
on)
18-08) D 11/9/2017 19:16
Xo (in.) Bolt#1 Bolt#2 Bolt Dist. to X,Y axis: Bolt No.: ### ###
Bolt Group Properties: S Xo = S Yo = Xc = Yc = S Ix = S Iy = J= S Ixy = q= S Pz = S Px = S Py =
e to and from the concrete.
S Mx = S My =
forcement (Section D.4.2.1)
S Mz = ###
APPENDIX D:
C, D, E, or F. (Sect. D3.3) ###
ents having a minimum Steel f Factor Selection:
einforcement is provided
Tension Ductile Brittle
Concrete f Factor Selection: Condition A Shear Loads
Cast-in:
0.75 (continued)
2. Section D.5.2: Anc,max = Edges = hef =
4. Section D.5.4: ca1 = ca2 = ca2 / ca1= Factor = Single or Group? (if Cmin < 1.5hef)
Nu,max =
sx1 = sy1 = cx1 = cx2 = cy1 =
0.7 Yc,V= CASE 1:
CASE 2:
CASE 3:
0.7 CASE 2:
Vu(-)x = Yec,V= Yed,V= Yh,V= ca1 = ca2(a) = ca2(b) =
AVC = AVCO = 0.7 Vcbg,x =
Influence Edges? CASE 2:
Vu(+)x = Yec,V= Yed,V= Yh,V= 0.65 ca2(a) = (continued)
AVC = AVCO = Vb = Vcbg,x = Influence Edges? CASE 2:
Vu(+)y = Yec,V= Yed,V= Yh,V= ca1 = ca2(a) = ca2(b) =
AVC = AVCO = Vb =
b))) x MIN(1.5*ca1,ha)
Vcbg,y = Vcbg,x =
0.7 CASE 2:
Vu(+)y = Yec,V= Yed,V= Yh,V= ca1 =
b))) x MIN(1.5*ca1,ha)
ca2(a) = ca2(b) =
AVC = 0.7 Vb = Vcbg,y = 0.7
0.7
6.2.1, 3rd paragraph)
0.7
(continued)
f anchor in tension
strength of Headed anchor
f anchor in shear - perp.
f anchor in shear - parallel
nchor in shear
See Section 7.7 else.
Program Environment:
Microsoft Office Excel 2003
Creation Date:
May 29th, 2009
Design References:
1. ACI 318-08 2. PCI Design Handbook, 6th Edition
This program is a workbook consisting of three (3) worksheets, described as follows: Worksheet Name
Description
DOC
This documentation sheet
EMBEDPL
Embedment Strength of (4) stud plate
EMBEDPL (2)
Embedment Strength of (2) stud plate
REVISION 1.4: (8/30/2013) Fixed glitch on eccentricity with and without tension. Program Assumptions and Limitations: 1. This spreadsheet program is intended to analyze and design the embedment of four headed concrete anchors affixed to a rigid plate. Shear and tension embedment strength is calculated per Appendix D of ACI 318. The bearing capacity is calculated per Section 10 & 11 of ACI 318. 2. This program assumes that the anchor strength is not governed by ductile yielding of the anchored steel which would cause significant redistribution of anchor forces and that the attachment that distributes the loads to the anchors is sufficiently stiff. 3. The required strength is calculated from the applicable load combinations in Section 9.2. 4. This spreadsheet, as well as the provisions of Appendix D, do not apply to the design of anchors in hinge zones of concrete structures under seismic loads. 5. This program assumes that the studs are not post-tensioned, post-installed, or torqued controlled anchors. However for conservative calculations, the minimum edge distance required uses limitation for torque controlled anchors (actual minimum edge distance per section 7.7) 6. This program assumes that the member clear cover is 2 inches for the purpose of punching shear calculations. 7. This program does not afford entry of eccentricity in the z-axis. 8. This program does not for strength of the plate itself or the welding affixing the studs to the plate. 9. This program contains numerous “comment boxes” which contain a wide variety of information including explanations of input or output items, equations used, data tables, etc. (Note: presence of a “comment box” is denoted by a “red triangle” in the upper right-hand corner of a cell. Merely move the mouse pointer to the
desired cell to view the contents of that particular "comment box".)
Program Theory and Operation: The top left of the spreadsheet screen allows for input of required information in lightly yellow highlighted boxes. Information required includes the following:
Anchorage Spreadsheet: Input: 1. Loads: a. Nua (Ultimate Factored Tensile Load) in kips b. Vua (Ultimate Factored Shear Load) in kips in the x direction c. Vua (Ultimate Factored Shear Load) in kips in the y direction d. ex, Eccentricity of load about the x-axis d. ey, Eccentricity of load about the y-axis 2. Dimensions: a. bx1, Steel edge distance: distance from the centerline of bolt to the edge of plate in x direction. b. bx2, Steel edge distance: distance from the centerline of bolt to the edge of plate in x direction. c. by1, Steel edge distance: distance from the centerline of bolt to the edge of plate in y direction. d. by2, Steel edge distance: distance from the centerline of bolt to the edge of plate in y direction. e. sx1, Stud spacing distance: distance between the centerline of bolts in x direction. f. sy1, Stud spacing distance: distance between the centerline of bolts in y direction. [only in "EMBEDPL"] g. cx1, Concrete edge distance: distance from the centerline of bolt to the edge in x direction. h. cx2, Concrete edge distance: distance from the centerline of bolt to the edge in x direction. i. cy1, Concrete edge distance: distance from the centerline of bolt to the edge in y direction. j. cy2, Concrete edge distance: distance from the centerline of bolt to the edge in y direction. 3. Parameters : a. Stud Anchor Diameter, db b. Specified Compressive strength of Concrete, f'c c. Specified Yield strength of anchor steel, fy d. Specified Tensile strength of anchor steel, futa e. Steel element, Ductile or Brittle: per Section D.1 f. The overall depth through which the anchor transfers force to and from the concrete, hef g. Thickness of member in which an anchor is located, ha h. Potential Failure Surfaces crossed by supplementary reinforcement (Section D.4.2.1) i. Is there anticipation of cracking at service levels (See Section D.6.2.7)? j. Are anchors are located in structure assigned to Seismic Design Category C, D, E, or F. (Sect. D3.3)? k. Concrete Type per Section 2.2. l. Per Section D.6.2.3? For cast-in headed studs that are continuously welded to steel attachments having a minimum thickness of > 3/8" and db/2 provided that: (a) spacing > 2.5 in. and (b) reinforcement is provided at the corners if ca2 < 1.5hef.
Output: 1. Steel strength of anchor in tension: (SEC D.5.1)
Nsa =
nAse,Vfuta
2. Concrete Breakout strength of anchor in tension: (SEC D.5.2)
Ncb =
Anc
Yed,NYc,NY,NNb
Single Anchor
Yec,NYed,NYc,NY,NNb
Group of Anchors
Anco Ncbg =
Anc Anco
3. Pullout strength of anchor in tension: (SEC D.5.3)
Npn =
Yc,PNp
Np =
Abrg8f'c
Single Anchor
4. Concrete Side-Face Blowout strength of Headed anchor in tension: (SEC D.5.4)
Nsb =
160ca1Abrg1/2f'c1/2
For cast-in headed stud anchors
5. Steel strength of anchor in shear: (SEC D.6.1)
Vsa =
nAse,Vfuta
6. Concrete Breakout strength of anchor in shear: (SEC D.6.2)
Vcb =
Avc
Single Anchor
Avco Group of Anchors
Vcb =
Av
Yec,V Yed,VYc,VYh,VVb
Avco 7. Concrete Pryout strength of anchor in shear: (SEC D.6.3)
V =
kNcb
Vg =
kNcbg
8. Interaction of tensile and shear forces: (SEC D.7)
if Vua < 0.2fVn
fNn > NUA
if Nua < 0.2fNn
fVn > VUA
if Nua > 0.2fNn & Vua > 0.2fVn
NUA ΦNn
9. Required edge distances & spacings: (ACI 318-08 Section D.7 & ASIC Table J3.4)
See Calculated section 10. Plate Bearing: (ACI 318-08 Section 10.14)
A1 = (bx1 + cx1 + bx2)(by1 + sy1 + by2) A2 = (cx1 + cx1 + cx2)(cy1 + sy1 +cy2) Multiplication Factor = (A2/A1)^0.5 < 2.0 ΦPn = Φ0.85fc'A1 x (Multiplication Factor) 11. Plate Punching Shear: (ACI 318-08 Section 11.12.2.1)
bo = (bx1 + cx1 + bx2) + (by1 + sy1 + by2) d = ha - 2in. (Assume 2" clear cover) b = Length of: Long side of plate / Short side of plate Factor = Minimum of (2 + 4/b) or 4 Vc = Factor x (fc')^0.5 x bo x d
+
VUA ΦVn
<
1.2
EMBEDMENT PLATE CALCULATION (Demo Version)
Job Name: Job Number:
Per Building Code Requirements for Structural Concrete (ACI 318-08) Design of (4) Stud Embed Plate Anchorage per Appendix D Subject: Date: Originator: Checker:
Input Data: Loads: Nua =
9
kips
Vua,x =
0
kips
Vua,y =
2 1 1.5
kips
ex = ey =
(Tension)
in. in.
Dimensions: bx1 = bx2 =
2 2
in.
PL Edge Distance
in.
PL Edge Distance
by1 =
2
in.
PL Edge Distance
by2 =
2
in.
PL Edge Distance
sx1 = sy1 = cx1 = cx2 = cy1 = cy2 =
4 4 48 48 4 12
in.
Spacing in x-dir.
in.
Spacing in y-dir.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
#1: #2:
Parameters: Anchor Dia., db = Concrete, f'c=
#3:
Stud Reactions (k) Axial Rz Shear Rh 0.56 0.40 -1.69 0.64 -2.81 0.40 -5.06 0.64
1/2 3000
in.
Stud Anchor Diameter
psi
Specified Compressive strength of Concrete
Anchor, fy =
51
ksi
Specified Yield strength of anchor steel
Anchor, futa =
65
ksi
Specified Tensile strength of anchor steel
Steel Element = Embedment, hef = Thickness, ha = Supp. Reinf.? Cracking Anticip.? Seismic (Chapt.21) Concrete Type = Per Sect. D.6.2.3?
Ductile
#4:
(Section D.1)
4
in.
The overall depth through which the anchor transfers force to and from the concrete.
6 Yes No No
in.
Thickness of member in which an anchor is located,
Normalwt Yes
Potential Failure Surfaces crossed by supplementary reinforcement (Section D.4.2.1) Cracking at service levels (Section D.6.2.7
Case?
Case 2
Anchors are located in structure assigned to Seismic Design Category C, D, E, or F. (Sect. D3.3) (Section 2.2) For cast-in headed studs that are continuously welded to steel attachments having a minimum thickness of > 3/8" and db/2 provided that: (a) spacing > 2.5 in. and (b) reinforcement is provided at the corners if ca2 < 1.5hef.
Results: 1. Steel strength of anchor in tension: (Section D.5.1) Nsa =Asefuta (Equation D-3)
Ase, N =
0.2
in2
Nsa =
13.00
kips
ΦNsa =
9.75
kips / bolt
Effective Cross Sectional Area of Anchor
Φ= Nu,max =
5.06
kips
=>
OK
2. Concrete Breakout strength of anchor in tension: (Section D.5.2) Ncbg = Anc Yec,NYed,NYc,NY,NNb (Equation D-5) Anco Anc =
224.00
in2
Anco =
144.00
in2
Yec,N(x-dir) =
Anco = 9hef2 Yec,N =
0.87
1
<1
Yec,N(y-dir) =
0.92
Yec,N(comb.) =
0.80
Yed,N =
0.90
e'Nx
=
1.29
in
Eccentricity of all tension forces on a group of anchors in the x dir.
e'Ny
=
0.82
in
Eccentricity of all tension forces on a group of anchors in the y dir.
Yc,N =
1.25
Yc,N = 1.25 for Cast-in-place anchors
Y,N =
1 1
Y,N = 1.0 for Cast-in-place anchors
l= kc = Nb =
24 10.52
(1 + 2e'N 3hef Yed,N = 1 (if Cmin > 1.5hef ) -OR-
kips
) 0.7 + 0.3cmin / (1.5 hef)
kc = 24 for Cast-in-place anchors Nb = klf'c1/2hef3/2 Nb,max = 16lf'c1/2hef5/3 if 11in. < hef < 25in. Φ=
ΦNcbg =
11.06
Nua =
kips
3. Pullout strength of anchor in tension: (Section D.5.3) Npn =Yc,PNp Abrg =
0.59
Np =
14.16
Yc,P=
1.40
ΦNpn =
14.87
9.00
kips
=>
OK
(Equation D-14)
in2
Np =Abrg8f'c
(Equation D-15)
Φ= kips / bolt
Nu,max =
5.06
kips
=>
OK
4. Concrete Side-Face Blowout strength of Headed anchor in tension: (Section D.5.4) Nsb = 160ca1Abrg1/2lf'c1/2 (Equation D-17) Nsbg = (1 + s/6ca1)Nsb
(Equation D-18)
Ca1 =
4.00
Ca2 =
48.00
Ca2 / Ca1 =
3.00
Factor = Nsb =
1.00 N/A
kips
Ca1 > 0.4 hef => Not Applicable (Section D.5.4.1)
Nsbg =
N/A
kips
Ca1 > 0.4 hef and/or s > 6ca1=> Not Applicable (Section D.5.4.2)
ΦN =
N/A
kips
1.0 < Ca2 / Ca1 < 3.0
Nu,max =
1.69
kips
=>
Φ=
N/A
5. Steel strength of anchor in shear: (Section D.6.1) Vsa =Ase,Vfuta Ase,V =
0.20
in2
futa =
65.00
ksi
Vsa =
13.00
kips/bolt
ΦVsa =
8.45
kips/bolt
(Equation D-19)
Effective Cross Sectional Area of Anchor
Φ= Vu,max =
0.64
kips
=>
OK
6. Concrete Breakout strength of anchor in shear: (Section D.6.2)* Vb = 8 (le/da)0.2da1/2lf'c1/2Ca11.5 Vcbg =
(Equation D-25)
Yec,VYed,VYc,VYh,VVb
Avc
(Equation D-22)
Avco ha =
6.00
in
Thickness of member in which an anchor is located
le =
4.00
in
Load bearing length (le = minimum of hef or8 da))
da =
0.50
in
da = db (Outside diameter of shaft of headed stud)
e'vx
=
1.00
in
Eccentricity of shear force on a group of anchors in the x dir.
e'vy
=
1.50
in
Eccentricity of shear force on a group of anchors in the y dir.
l= Yc,V=
1
Yed,V=
N/A
Yed,V = 1 (if ca2 > 1.5ca1) or 0.7 + 0.3ca2/(1.5ca1)
Yh,V=
N/A
Yh,V = (1.5ca1/ha)^0.5 < 1.0
AVC =
N/A
in2
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1,sy1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*ca1,ha)
AVCO =
N/A
in2
AVCO = 4.5(ca1)^2
Vb =
N/A
kips
Vcbg,x =
N/A
kips
ΦVcbg,x =
N/A
kips
Concrete Type Modification Factor
1.40 Cracking Modification Factor (per Section D.6.2.7) X - Direction (perpendicular to edge): N/A ca1 = in ca1 = (cx1 or cx2) + sx1 or minimum required per Section D.6.2.4 Yec,V= Yec,V = 1 / (1+2e'v,y/(3ca1)) N/A
Φ= Vu,max =
N/A
kips
=>
N/A
Y - Direction (perpendicular to edge): ca1 =
16.00
in
ca1 = (cy1 or cy2) + sy1 or minimum required per Section D.6.2.4
Yec,V=
0.96
Yec,V = 1 / (1+2e'v,y/(3ca1))
Yed,V=
1.00
Yed,V = 1 (if ca2 > 1.5ca1) or 0.7 + 0.3ca2/(1.5ca1)
Yh,V=
1.00
Yh,V = (1.5ca1/ha)^0.5 < 1.0
AVC =
312.00
in2
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1,sy1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*ca1,ha)
AVCO =
1152.00
in2
AVCO = 4.5(ca1)^2
Vb =
30.06
kips
Vcbg,y =
10.94
kips
ΦVcbg,y =
8.21
kips
X - Direction (parallel to edge): Vcbg,x = 12.02 kips ΦVcbg,x =
9.02 kips Y - Direction (parallel to edge): Vcbg,y = 8.82 kips
0.2 1/2 1/2 1.5 Vb = 8 (le/da) da lf'c Ca1
Φ= Vu,max =
2.00
kips
=>
OK Φ=
Per Section D.6.2.1.(c)
Vu,max =
N/A
kips
=>
N/A Φ=
Per Section D.6.2.1.(c)
Vu,max = OK 6.61 2.00 kips => kips *NOTE: Case 1 calculation (evaluation of bolt to closest edge) not req'd. (See Section RD6.2.1, 3rd paragraph) ΦVcbg,y =
7. Concrete Pryout strength of anchor in shear: (Section D.6.3) Vg =kNcbg
(Equation D-31)
k =
2.00
Ncbg =
14.74
kips
Vg =
29.48
kips
ΦVg =
22.11
kips
k = 1.0 (for hef < 2.5in.); k = 2.0 (for hef > 2.5in.) from Equation D-5 (See previous Section D.5.2 calcs)
Φ= Vu,max =
2.07
kips
=>
Vu,max = sum of each bolt shear
OK
8. Interaction of tensile and shear forces: (Section D.7)
NUA
Tension Ratio =
ΦNn Steel: Breakout: Pullout: Sideface Blowout:
0.519 0.814 0.340 N/A
Steel strength of anchor in tension Concrete Breakout strength of anchor in tension Pullout strength of anchor in tension Concrete Side-Face Blowout strength of Headed anchor in tension
VUA
Shear Ratio =
ΦVn Steel: Breakout (Case2): Breakout (Case3): Pryout:
NUA
Combined Stress Ratio (CSR) =
ΦNn CSR:
0.075 0.244 0.302 0.093
+
Steel strength of anchor in shear Concrete Breakout strength of anchor in shear - perp. Concrete Breakout strength of anchor in shear - parallel Concrete Pryout strength of anchor in shear
VUA ΦVn
<
1.2
1.12
OK
EMBEDMENT STRENGTH (Per ACI 318-08 - Appendix D) 9. Required edge distances & spacings: (ACI 318-08 Section D.7 & ASIC Table J3.4) smin =
2.00
in
Minimum spacing =
sact =
4.00 3.00
in
Actual lesser of two spacings, sy1 & sx1
in
Assume torqued cast-in headed anchors (conservative). See Section 7.7 else.
4.00 0.88
in
Actual lesser of four edge distances, cy1/2 & cx1/2
in
Minimum steel edge distance per Table J3.4
in
Actual lesser of four edge distances, cy1/2 & cx1/2
Req'd thick., ha,min =
2.00 4.75
in.
ha,min = hef + 0.75"
Actual thickness, ha =
6.00
in.
Conc. Edge dist, min = Conc. Edge dist, act = Edge dist, min = Edge dist, act =
smin = 4 x da (for untorqued cast-in-place anchors)
OK OK OK OK
10. Plate Bearing: (ACI 318-08 Section 10.14) 64.00 in2 Plate Area, A1 = A1 = (bx1 + sx1 + bx2)(by1 + sy1 + by2) 2 Concrete Area, A2 = 2000.00 in A2 = (cx1 + sx1 + cx2)(cy1 + sy1 +cy2) 2.00 Multiplication Factor = Multiplication Factor = (A2/A1)^0.5 < 2.0 326.40 kips Pn = Pn = 0.85fc'A1 x (Multiplication Factor) ΦPn =
212.16
kips
Nua =
N/A
kips
=>
11. Plate Punching Shear: (ACI 318-08 Section 11.12.2.1) 16.00 Perimeter, bo = in bo = (bx1 + sx1 + bx2) + (by1 + sy1 + by2) 4.00 Concrete depth, d = in d = ha - 2in. (Assume 2" clear cover) 1.00 b= b = Length of: Long side of plate / Short side of plate
N/A
Factor = Vc = ΦVc =
4.00 14.02
kips
9.11
kips
Factor = Minimum of (2 + 4/b) or 4 Vc = Factor x (fc')^0.5 x bo x d
Nua =
N/A
kips
=>
N/A
on)
18-08) D 11/9/2017 19:16
Xo (in.) Bolt#1 Bolt#2 Bolt#3 Bolt#4 Bolt Dist. to X,Y axis: Bolt No.: ### ### ### ### Bolt Group Properties: S Xo = S Yo = Xc = Yc = S Ix = S Iy = J= S Ixy = q= S Pz = S Px = S Py = S Mx =
e to and from the concrete.
S My = S Mz =
forcement (Section D.4.2.1)
###
APPENDIX D:
C, D, E, or F. (Sect. D3.3)
###
Steel f Factor Selection:
ents having a minimum
einforcement is provided
Tension Ductile Brittle
Concrete f Factor Selection: Condition A Shear Loads
Cast-in:
0.75 (continued)
2. Section D.5.2: Anc,max = Edges = hef =
4. Section D.5.4: ca1 = ca2 = ca2 / ca1= Factor = Single or Group? (if Cmin < 1.5hef)
Nu,max =
sx1 = sy1 = cx1 = cx2 = cy1 =
0.75 Yc,V= CASE 1:
CASE 2:
CASE 3:
0.75 CASE 2:
Vu(-)x = Yec,V= Yed,V= Yh,V= ca1 = ca2(a) = ca2(b) =
AVC = AVCO = 0.75 Vcbg,x =
Influence Edges? CASE 2:
Vu(+)x = Yec,V= Yed,V= Yh,V= 0.65 ca2(a) = (continued)
AVC = AVCO = Vb = Vcbg,x = Influence Edges? CASE 2:
Vu(+)y = Yec,V= Yed,V= Yh,V= ca1 = ca2(a) = ca2(b) =
AVC = AVCO = Vb =
a2(b))) x MIN(1.5*ca1,ha)
Vcbg,y = Vcbg,x =
0.75 CASE 2:
Vu(+)y = Yec,V= Yed,V= Yh,V= ca1 =
a2(b))) x MIN(1.5*ca1,ha)
ca2(a) = ca2(b) =
AVC = 0.75 Vb = Vcbg,y = 0.75
0.75
6.2.1, 3rd paragraph)
0.75
(continued)
f anchor in tension
strength of Headed anchor
f anchor in shear - perp.
f anchor in shear - parallel
nchor in shear
See Section 7.7 else.
EMBEDMENT PLATE CALCULATION (Demo Version)
Job Name: Job Number:
Per Building Code Requirements for Structural Concrete (ACI 318-08) Design of (2) Stud Embed Plate Anchorage per Appendix D Subject: Date: Originator: Checker:
Input Data: Loads: Nua =
6.5
kips
Vua,x =
1
kips
Vua,y =
kips
ex = ey =
5 1 0
Dimensions: bx1 = bx2 =
2 2
in.
PL Edge Distance
in.
PL Edge Distance
by1 =
2
in.
PL Edge Distance
by2 =
2
in.
PL Edge Distance
sx1 = cx1 = cx2 = cy1 = cy2 =
4 48 48 12 44
in.
Spacing in x-dir.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
in.
Edge Distance to Conc.
(Tension)
in. in.
#1:
Parameters: Anchor Dia., db = Concrete, f'c= Anchor, fy = Anchor, futa = Steel Element =
#2:
Stud Reactions (k) Axial Rz Shear Rh -1.62 1.35 -4.88 3.78
1/2 3000 51
in.
Stud Anchor Diameter
psi
Specified Compressive strength of Concrete
ksi
Specified Yield strength of anchor steel
65
ksi
Specified Tensile strength of anchor steel
Ductile
(Section D.1)
Embedment, hef = Thickness, ha =
4
in.
The overall depth through which the anchor transfers force to and from the concrete.
6
in.
Thickness of member in which an anchor is located,
Supp. Reinf.? Cracking Anticip.? Seismic (Chapt.21) Concrete Type = Per Sect. D.6.2.3?
No No No Normalwt No
Potential Failure Surfaces crossed by supplementary reinforcement (Section D.4.2.1) Cracking at service levels (Section D.6.2.7)
Case?
Case 3
Anchors are located in structure assigned to Seismic Design Category C, D, E, or F. (Sect. D3.3) (Section 2.2) For cast-in headed studs that are continuously welded to steel attachments having a minimum thickness of > 3/8" and db/2 provided that: (a) spacing > 2.5 in. and (b) reinforcement is provided at the corners if ca2 < 1.5hef.
Results: 1. Steel strength of anchor in tension: (Section D.5.1) Nsa =Asefuta (Equation D-3)
Ase, N =
0.2
in2
Nsa =
13.00
kips
ΦNsa =
9.75
kips / bolt
Effective Cross Sectional Area of Anchor
Φ= Nu,max =
4.88
kips
=>
OK
2. Concrete Breakout strength of anchor in tension: (Section D.5.2) Ncbg = Anc Yec,NYed,NYc,NY,NNb (Equation D-5) Anco Anc =
192.00
in2
Anco =
144.00
in2
Yec,N(x-dir) =
Anco = 9hef2 Yec,N =
0.90
1
<1
Yec,N(y-dir) =
1.00
Yec,N(comb.) =
0.90
Yed,N =
1.00
e'Nx
=
1.00
in
Eccentricity of all tension forces on a group of anchors in the x dir.
e'Ny
=
0.00
in
Eccentricity of all tension forces on a group of anchors in the y dir.
Yc,N =
1.25
Yc,N = 1.25 for Cast-in-place anchors
Y,N =
1 1
Y,N = 1.0 for Cast-in-place anchors
l= kc = Nb =
24 10.52
(1 + 2e'N 3hef Yed,N = 1 (if Cmin > 1.5hef ) -OR-
kips
) 0.7 + 0.3cmin / (1.5 hef)
kc = 24 for Cast-in-place anchors Nb = klf'c1/2hef3/2 Nb,max = 16lf'c1/2hef5/3 if 11in. < hef < 25in. Φ=
ΦNcbg =
11.04
Nua =
kips
3. Pullout strength of anchor in tension: (Section D.5.3) Npn =Yc,PNp Abrg =
0.59
Np =
14.16
Yc,P=
1.40
ΦNpn =
13.88
6.50
kips
=>
OK
(Equation D-14)
in2
Np =Abrg8f'c
(Equation D-15)
Φ= kips
Nu,max =
4.88
kips
=>
OK
4. Concrete Side-Face Blowout strength of Headed anchor in tension: (Section D.5.4) Nsb = 160ca1Abrg1/2lf'c1/2 (Equation D-17) Nsbg = (1 + s/6ca1)Nsb
(Equation D-18)
Ca1 =
12.00
Ca2 =
48.00
Ca2 / Ca1 =
3.00
Factor = Nsb =
1.00 N/A
kips
Ca1 > 0.4 hef => Not Applicable (Section D.5.4.1)
Nsbg =
N/A
kips
Ca1 > 0.4 hef and/or s > 6ca1=> Not Applicable (Section D.5.4.2)
ΦN =
N/A
kips
1.0 < Ca2 / Ca1 < 3.0
Nu,max =
4.88
kips
=>
Φ=
N/A
5. Steel strength of anchor in shear: (Section D.6.1) Vsa =Ase,Vfuta Ase,V =
0.20
in2
futa =
65.00
ksi
Vsa =
13.00
kips/bolt
ΦVsa =
8.45
kips/bolt
(Equation D-19)
Effective Cross Sectional Area of Anchor
Φ= Vu,max =
3.78
kips
=>
OK
6. Concrete Breakout strength of anchor in shear: (Section D.6.2)* Vb = 7 (le/da)0.2da1/2lf'c1/2Ca11.5 Vcbg =
Yec,VYed,VYc,VYh,VVb
Avc
(Equation D-24) (Equation D-22)
Avco ha =
6.00
in
Thickness of member in which an anchor is located
le =
4.00
in
Load bearing length (le = minimum of hef or8 da))
da =
0.50
in
da = db (Outside diameter of shaft of headed stud)
e'vx
=
1.00
in
Eccentricity of shear force on a group of anchors in the x dir.
e'vy
=
0.00
in
Eccentricity of shear force on a group of anchors in the y dir.
l= Yc,V=
1
Yed,V=
0.77
Yed,V = 1 (if ca2 > 1.5ca1) or 0.7 + 0.3ca2/(1.5ca1)
Yh,V=
1.00
Yh,V = (1.5ca1/ha)^0.5 < 1.0
AVC =
336.00
in2
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*ca1,ha)
AVCO =
5000.00
in2
AVCO = 4.5(ca1)^2
Vb =
79.08
kips
Vcbg,x =
5.74
kips
ΦVcbg,x =
4.02
kips
Concrete Type Modification Factor
1.40 Cracking Modification Factor (per Section D.6.2.7) X - Direction (perpendicular to edge): 33.33 ca1 = in ca1 = (cx1 or cx2) + sx1 or minimum required per Section D.6.2.4 Yec,V= Yec,V = 1 / (1+2e'v,y/(3ca1)) 1.00
Φ= Vu,max =
1.00
kips
=>
OK
Y - Direction (perpendicular to edge): ca1 =
32.00
in
ca1 = (cy1 or cy2) or minimum required per Section D.6.2.4
Yec,V=
0.98
Yec,V = 1 / (1+2e'v,y/(3ca1))
Yed,V=
1.00
Yed,V = 1 (if ca2 > 1.5ca1) or 0.7 + 0.3ca2/(1.5ca1)
Yh,V=
1.00
Yh,V = (1.5ca1/ha)^0.5 < 1.0
AVC =
600.00
AVCO =
4608.00
in2 in
2
Vb =
74.39
kips
Vcbg,y =
13.28
kips
ΦVcbg,y =
9.30
kips
X - Direction (parallel to edge): Vcbg,x = 16.78 kips ΦVcbg,x =
11.75 kips Y - Direction (parallel to edge): Vcbg,y = 12.40 kips
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*ca1,ha) AVCO = 4.5(ca1)^2 0.2 1/2 1/2 1.5 Vb = 7 (le/da) da lf'c Ca1
Φ= Vu,max =
5.00
kips
=>
OK Φ=
Per Section D.6.2.1.(c)
Vu,max =
1.00
kips
=>
OK Φ=
Per Section D.6.2.1.(c)
Vu,max = OK 8.68 5.00 kips => kips *NOTE: Case 1 calculation (evaluation of bolt to closest edge) not req'd. (See Section RD6.2.1, 3rd paragraph) ΦVcbg,y =
7. Concrete Pryout strength of anchor in shear: (Section D.6.3) Vg =kNcbg
(Equation D-31)
k =
2.00
Ncbg =
15.77
kips
Vg =
31.55
kips
ΦVg =
22.08
kips
k = 1.0 (for hef < 2.5in.); k = 2.0 (for hef > 2.5in.) from Equation D-5 (See previous Section D.5.2 calcs)
Φ= Vu,max =
5.13
kips
=>
Vu,max = sum of each bolt shear
OK
8. Interaction of tensile and shear forces: (Section D.7)
NUA
Tension Ratio =
ΦNn Steel: Breakout: Pullout: Sideface Blowout:
0.500 0.589 0.351 N/A
Steel strength of anchor in tension Concrete Breakout strength of anchor in tension Pullout strength of anchor in tension Concrete Side-Face Blowout strength of Headed anchor in tension
VUA
Shear Ratio =
ΦVn Steel: Breakout (Case2): Breakout (Case3): Pryout:
NUA
Combined Stress Ratio (CSR) =
ΦNn CSR:
0.448 0.538 0.576 0.232
+
Steel strength of anchor in shear Concrete Breakout strength of anchor in shear - perp. Concrete Breakout strength of anchor in shear - parallel Concrete Pryout strength of anchor in shear
VUA ΦVn
<
1.2
1.16
OK
EMBEDMENT STRENGTH (Per ACI 318-08 - Appendix D) 9. Required edge distances & spacings: (ACI 318-08 Section D.7 & ASIC Table J3.4) smin =
2.00
in
Minimum spacing =
sact =
4.00 3.00
in
Actual lesser of spacing, sx1
in
Assume torqued cast-in headed anchors (conservative). See Section 7.7 else.
in
Actual lesser of four edge distances, cy1/2 & cx1/2
Edge dist, min =
12.00 0.88
in
Minimum steel edge distance per Table J3.4
Edge dist, act =
2.00
in
Actual lesser of four edge distances, cy1/2 & cx1/2
Req'd thick., ha,min =
4.75
in
ha,min = hef + 0.75"
Actual thickness, ha =
6.00
in
Conc. Edge dist, min = Conc. Edge dist, act =
smin = 4 x da (for untorqued cast-in-place anchors)
OK OK OK OK
10. Plate Bearing: (ACI 318-08 Section 10.14) 32.00 in2 Plate Area, A1 = A1 = (bx1 + sx1 + bx2)(by1 + by2) 2 Concrete Area, A2 = 5600.00 in A2 = (cx1 + sx1 + cx2)(cy1 + cy2) 2.00 Multiplication Factor = Multiplication Factor = (A2/A1)^0.5 < 2.0 163.20 kips Pn = Pn = 0.85fc'A1 x (Multiplication Factor) ΦPn =
106.08
kips
Nua =
N/A
11. Plate Punching Shear: (ACI 318-08 Section 11.12.2.1) 12.00 Perimeter, bo = in bo = (bx1 + sx1 + bx2) + (by1 + by2) 4.00 Concrete depth, d = in d = ha - 2in. (Assume 2" clear cover)
kips
=>
N/A
b= Factor = Vc = ΦVc =
2.00 4.00 10.52
kips
6.84
kips
b = Length of: Long side of plate / Short side of plate Factor = Minimum of (2 + 4/b) or 4 Vc = Factor x (fc')^0.5 x bo x d
Nua =
N/A
kips
=>
N/A
on)
18-08) D 11/9/2017 19:16
Xo (in.) Bolt#1 Bolt#2 Bolt Dist. to X,Y axis: Bolt No.: ### ###
Bolt Group Properties: S Xo = S Yo = Xc = Yc = S Ix = S Iy = J= S Ixy = q= S Pz = S Px = S Py =
e to and from the concrete.
S Mx = S My =
forcement (Section D.4.2.1)
S Mz = ###
APPENDIX D:
C, D, E, or F. (Sect. D3.3) ###
ents having a minimum Steel f Factor Selection:
einforcement is provided
Tension Ductile Brittle
Concrete f Factor Selection: Condition A Shear Loads
Cast-in:
0.75 (continued)
2. Section D.5.2: Anc,max = Edges = hef =
4. Section D.5.4: ca1 = ca2 = ca2 / ca1= Factor = Single or Group? (if Cmin < 1.5hef)
Nu,max =
sx1 = sy1 = cx1 = cx2 = cy1 =
0.7 Yc,V= CASE 1:
CASE 2:
CASE 3:
0.7 CASE 2:
Vu(-)x = Yec,V= Yed,V= Yh,V= ca1 = ca2(a) = ca2(b) =
AVC = AVCO = 0.7 Vcbg,x =
Influence Edges? CASE 2:
Vu(+)x = Yec,V= Yed,V= Yh,V= 0.65 ca2(a) = (continued)
AVC = AVCO = Vb = Vcbg,x = Influence Edges? CASE 2:
Vu(+)y = Yec,V= Yed,V= Yh,V= ca1 = ca2(a) = ca2(b) =
AVC = AVCO = Vb =
b))) x MIN(1.5*ca1,ha)
Vcbg,y = Vcbg,x =
0.7 CASE 2:
Vu(+)y = Yec,V= Yed,V= Yh,V= ca1 =
b))) x MIN(1.5*ca1,ha)
ca2(a) = ca2(b) =
AVC = 0.7 Vb = Vcbg,y = 0.7
0.7
6.2.1, 3rd paragraph)
0.7
(continued)
f anchor in tension
strength of Headed anchor
f anchor in shear - perp.
f anchor in shear - parallel
nchor in shear
See Section 7.7 else.
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