"EMBEDPL2" --- Embedment Strength of stud plate Program Description: "EMBEDPL2.xls" "EMBEDPL2.xls" is a MS-Excel spreadsheet workbook for the analysis of (2 ) Headed Concrete Anchors, HCA, per ACI 318-08, Appendix D. The spreadsheet is designed to find the embedment strength in concrete for the required plate within certain certain concrete parameters. The spreadsheet is protected but with no password required. Program Environment:
Microsoft Office Excel 2003
Creation Date:
February 17th, 2011
Design References:
1. ACI 318-08 2. PCI Design Handbook, 6th Edition
This program is a workbook consisting of two (2) worksheets, described as follows: Worksheet Name DOC EMBEDPL (2)
Description This documentation sheet Embedment Strength of (2) stud plate
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 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 would cause significant redistribution 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 a re not post-tensioned, post-installed, or torqued controlled anchors. However for conservative calculations, the minimum edge distance required uses limitation for torque controlle 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 account 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 wide variety of information including explanations of input or output items, equations used, data tables, etc. (Note: presence of a “comment box” 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 "EMBED 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 e dge 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. 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 h minimum thickness of > 3/8" and db/2 provided that: (a) spacing > 2.5 in. and (b) reinforcement is at the corners if ca2 < 1.5hef.
Output: 1. Steel strength of anchor in tension: (SEC D.5.1)
Nsa =
nAse,Vf uta
2. Concrete Breakout strength of anchor in tension: (SEC D.5.2)
Ncb =
Anc
Yed,NYc,NYcp,NNb
Single Anchor
Yec,NYed,NYc,NYcp,NNb
Group of Anchors
Anco Ncbg =
Anc Anco
3. Pullout strength of anchor in tension: (SEC D.5.3)
Npn = Np =
Yc,PNp
Abrg8f'c
Single Anchor
4. Concrete Side-Face Blowout strength of Headed anchor in tension: (SEC D.5.4)
Nsb =
1/2
1/2
160ca1 Abrg f'c
For cast-in headed stud anchors
5. Steel strength of anchor in shear: (SEC D.6.1)
Vsa =
nAse,Vf uta
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)
Vcp =
kcpNcb
Vcpg =
kcpNcbg
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 > 0.2 fVn
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
PL"]
)? ving a rovided
< 1.2
EMBEDMENT PLATE CALCULATION
Job Name:
Per Build ing Code Requirem ents for Structural Concrete ( ACI 318-08) Design of (2) Stud Embed Plate Anchorage per Appendix D Subject: Date:
Job Number:
Originator:
Checker:
Input Data: Loads: Nua =
6.5
kips
Vua,x =
5
kips
Vua,y =
5
kips
ex = ey =
1 0
in.
Dimensions: bx1 = bx2 = by1 = by2 = sx1 = cx1 = cx2 = cy1 = cy2 =
2 2 2 2 4 48 48 12 44
in.
PL Edge Distance
in.
PL Edge Distance
in.
PL Edge Distance
in.
PL Edge Distance
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.
Parameters: Anchor Dia., db =
1/2
in.
Stud Anchor Diameter
Concrete, f'c= Anchor, f y =
3000 36
psi
Specified Compressive strength of Concrete
ksi
Specified Yield strength of anchor steel
Anchor, f uta =
58
ksi
Specified Tensile strength of anchor steel
Steel Element = Embedment, hef = Thickness, ha =
Stud Reactions (k) Axial Rz Shear Rh #1: -1.62 2.80 #2: -4.88 4.51
in.
The overall depth through which the anchor transfers force to and from t
12
in.
Thickness of member in which an anchor is located,
No
Cracking Anticip.?
No
Seismic (Chapt.21)
No
Per Sect. D.6.2.3?
in.
Ductile 9.5
Supp. Reinf.?
Concrete Type =
(Tension)
Normalwt No
(Section D.1)
Potential Failure Surfaces crossed by supplementary reinforcement (Sec 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. (S (Section 2.2) For cast-in headed studs that are continuously welded to steel attachments having a thickness of > 3/8" and db/2 provided that: (a) spacing > 2.5 in. and (b) reinforcement at the corners if ca2 < 1.5hef.
Results: 1. Steel strength of anchor in tension: (Section D.5.1) Nsa =Asef uta
(Equation D-3)
Ase, N = Nsa =
ΦNsa =
0.2
2
Effective Cross Sectional Area of Anchor
in
11.60
kips
8.70
kips
Φ= Nu,max =
4.88
=>
kips
OK
2. Concrete Breakout strength of anchor in tension: (Section D.5.2) Yec,NYed,NYc,NYcp,NNb Ncbg = Anc (Equation D-5) Anco Anc =
853.13
in
Anco =
812.25
in
Yec,N(x-dir) =
0.95
Yec,N(y-dir) =
1.00
Yec,N(comb.) =
0.95
Yed,N =
0.95
2
Anco = 9hef Yec,N =
<
1 2e'N
(1 +
)
3hef Yed,N = 1 or
if C min > 1.5h ef
0.7 + 0.3 cmin
if C min < 1.5h ef
1.5 hef Yc,N =
1.25
Yc,N = 1.25 for Cast-in-place anchors
Ycp,N =
1
Ycp,N = 1.0 for Cast-in-place anchors
l = kc =
1
Nb =
24 38.49
kc = 24 for Cast-in-place anchors Nb = klf'c1/2hef 3/2 Nb,max = 16lf'c1/2hef 5/3
kips
if 11in. < h ef < 25in.
Φ= ΦNcbg =
31.93
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
=>
(Equation D-14)
in
Np =Abrg8f'c
(Equation D-15)
Φ= Nu,max =
kips
4.88
kips
=>
4. Concrete Side-Face Blowout strength of Headed anchor in tension: (Section D.5.4) 1/2
1/2
Nsb = 160ca1 Abrg lf'c
(Equation D-17)
Nsbg = (1 + s/6ca1)Nsb
(Equation D-18)
Ca1 =
12.00
Ca2 =
48.00
OK
OK
Ca2 / Ca1 =
3.00
Factor =
1.00
Nsb =
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 =
5. Steel strength of anchor in shear: (Section D.6.1) Vsa =Ase,Vf uta Ase,V =
0.20
in
f uta =
58.00
ksi
Vsa =
11.60
kips/bolt
7.54
kips/bolt
ΦVsa =
4.88
kips
=>
Φ=
N/A
(Equation D-19)
Effective Cross Sectional Area of Anchor
Φ= Vu,max =
4.51
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 =
Avc
(Equation D-24)
Yec,VYed,VYc,VYh,VVb
(Equation D-22)
Avco ha =
12.00
in
Thickness of member in which an anchor is located
le =
4.00
in
Load bearing length (le = minimum of hef or 8 d a ))
da =
0.50
in
d a = d b (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 x dir.
l = Yc,V=
1
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 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 =
672.00
in
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*
AVCO =
5000.00
in
AVCO = 4.5(ca1)^2
Vb =
79.08
kips
Vcbg,x =
11.49
kips
8.04
kips
ΦVcbg,x =
Φ= Vu,max =
5.00
kips
=>
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
OK
AVC =
1200.00
in
AVC = (MIN(1.5ca1,ca2(a))+MIN(3ca1)+MIN(1.5ca1,ca2(b))) x MIN(1.5*
AVCO =
4608.00
in
AVCO = 4.5(ca1)^2
Vb =
74.39
kips
Vcbg,y =
26.57
kips
ΦVcbg,y =
18.60
kips
0.2
1/2
1/2
1.5
Vb = 7 (le/da) da lf'c Ca1
Φ= Vu,max =
5.00
kips
=>
OK
X - Direction (parallel to edge): Vcbg,x =
33.56
kips
ΦVcbg,x =
23.49
kips
Vu,max =
Y - Direction (parallel to edge): Vcbg,y = 24.80 kips
ΦVcbg,y =
17.36
Φ=
Per Section D.6.2.1.(c)
5.00
kips
=>
OK Φ=
Per Section D.6.2.1.(c)
Vu,max =
kips
5.00
kips
=>
OK
*NOTE: Case 1 calculation (evaluation of bolt to closest edge) not req'd. (See Section RD6.2.1, 3rd pa 7. Concrete Pryout strength of anchor in shear: (Section D.6.3) Vcpg =kcpNcbg kcp =
(Equation D-31)
kcp = 1.0 (for hef < 2.5in.); kcp = 2.0 (for hef > 2.5in.)
2.00
Ncbg =
45.61
kips
Vcpg =
91.21
kips
ΦVcpg =
63.85
kips
from Equation D-5 (See previous Section D.5.2 calcs)
Φ= Vu,max =
7.30
kips
=>
OK
Vu,max = sum of each bolt shear
8. Interaction of tensile and shear forces: (Section D.7) Tension Ratio =
NUA
ΦNn Steel: Breakout: Pullout: Sideface Blowout:
0.560 0.204 0.351 N/A
Steel strength of anchor in tension Concrete Breakout strength of anchor in ten Pullout strength of anchor in tension Concrete Side-Face Blowout strength of He in tension
Shear Ratio =
VUA
ΦVn Steel: Breakout (Case2): Breakout (Case3): Pryout: Combined Stress Ratio (CSR) =
NUA
ΦNn CSR:
0.598 0.622 0.288 0.114
+ 1.18
Steel strength of anchor in shear Concrete Breakout strength of anchor in she Concrete Breakout strength of anchor in she Concrete Pryout strength of anchor in shear
VUA
ΦVn
<
1.2
OK
EMBEDMENT STRENGTH (Per ACI 318-08 - Appendix D) 9. Required edge distances & spacings: (ACI 318-08 Section D.7 & ASIC Table J 3.4) smin =
2.00
in
Minimum spacing = smin = 4 x da (for untorqued cast-in-place anchors)
sact =
4.00
in
Actual lesser of spacing, sx1
Conc. Edge dist, min =
3.00
in
Assume torqued cast-in headed anchors (conservative). See Section 7.7
Conc. Edge dist, act =
12.00
in
Actual lesser of four edge distances, cy1/2 & cx1/2
Edge dist, min =
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 =
10.25
in
ha,min = hef + 0.75"
Actual thickness, ha =
12.00
in
10. Plate Bearing: (ACI 318-08 Plate Area, A1 = 32.00 5600.00 Concrete Area, A2 = Multiplication Factor = 2.00 Pn = 163.20 ΦPn =
106.08
17.09
OK OK OK
Section 10.14)
11. Plate Punching Shear: (ACI 12.00 Perimeter, bo = Concrete depth, d = 10.00 b = 2.00 4.00 Factor = Vc = 26.29 ΦVc =
OK
2
in
2
in
A1 = (bx1 + sx1 + bx2)(by1 + by2) A2 = (cx1 + sx1 + cx2)(cy1 + cy2) Multiplication Factor = (A2/A1)^0.5 < 2.0
kips
Pn = 0.85fc'A1 x (Multiplication Factor)
Nua =
kips
N/A
kips
=>
N/A
318-08 Sectio n 11.12.2.1) in
bo = (bx1 + sx1 + bx2) + (by1 + by2)
in
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 kips kips
Vc = Factor x (fc')^0.5 x bo x d
Nua =
N/A
kips
=>
N/A
Version 1.2
SUMMARY OF CHECKS: 11/17/2014 4:01 Row No.: Results:
Stress Ratio:
EMBEDMENT STRENGTH 49 72 80 92
Steel strength of anchor in tension Concrete Breakout strength of anchor in tension Pullout strength of anchor in tension Side-Face Blowout strength of anchor in tension
0.56 0.20 0.35 N/A
100
Steel strength of anchor in shear
0.60
123
Breakout strength of anchor in shear (X-Dir, Perp.)
0.62
133 Breakout strength of anchor in shear (Y-Dir, Perp.) 0.27 136 Breakout strength of anchor in shear (X-Dir, Parallel) 0.21 139 Breakout strength of anchor in shear (Y-Dir, Parallel) 0.29 148 Concrete Pryout strength of anchor in shear 0.11 170 Interaction of tensile and shear forces 1.18 DIMENSIONAL REQUIREMENTS 176 Minimum Spacing requirements SATISFACTORY 178 Minimum Concrete Edge distance SATISFACTORY 180 Minimum Steel Edge distance SATISFACTORY 181 Minimum Concrete Thickness SATISFACTORY CONCRETE 191 Compressive Bearing strength N/A 199 Plate Punching Shear N/A
e concrete.
tion D.4.2.1)
ect. D3.3)
inimum is provided
0.75
(continued)
0.7
0.7
0.7
0.65
(continued)
a1,ha)
0.7
a1,ha)
0.7
0.7
0.7
agraph)
0.7
(continued)
ion
ded anchor
ar - perp. ar - parallel
else.
