Specifications 0 8 2009 v
BUILDIDEC NG DIGARD
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ECLIPSE
ENGINEERING INC.
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Structural Calculations
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Steel Storage Racks
By Pipp Mobile Storage Systems, Inc.
Pipp P.O. #071368
True Religion Brand Jeans #5065
Washington Square (SO240872 -00) NOV 2
9585 SW Washington Square Rd. 2 5 009
- Spc. # B-12 QE D PROF
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Portland, OR 97223 , % 786 'P
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Prepared For: s faT , �
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Pipp M Storage Systems, Inc. ° 6," -. J ;ilk' s. 2966 Wilson Drive NW
• Walker, MI 49544 Expiration Date 11 i 2009
Please note: The calculations contained within justify the seismic resistance of
the shelving racks, the fixed and mobile base supports, and the connection to
the existing partition walls for both lateral and overturning forces as required
by the 2007 Oregon Structural Specialty Code. These storage racks are not
accessible to the general public.
� 9 t
155 NE REVERE AVENUE, SUITE. A. BEND. OR 97701 o '
PHONE: (5411 389 -9659 FAX: (541) 312-8708 ��U I-
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WWW.ECLI['SE- ENG1NEERING.COM \S � e
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Eclipse Engineering, Inc. True Religion Brand Jeans 11/25/2009
Engineer: Nick Bumam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE
Pipp Mobile STEEL STORAGE RACK DESIGN kips:= 1000•Ib
2006 IBC & 2007 CBC - 2208 & ACSE -7 - 15.5.3 lb
plf := ft —
Design Vertical Steel Posts at Each Corner :
Shelving Dimensions: psf:_ 1b
Total Height of Shelving Unit - h := 10.0.ft
lb
Width of Shelving Unit - w := 4.00.ft pcf = f-
Depth of Shelving Unit - d := 2.50.ft
Number of Shelves - N := 8 lb
ksi := 1000 • —
Vertical Shelf Spacing - S := 17.15.in in
Shelving Loads:
Maximum Live Load on each shelf is 50 Ibs:
Weight per shelf - W := 50•lb W = 501b
Load in P Sf - LLi . W W - LLi = 5•psf
Design Live Load on Shelf - LL := LL LL = 5.psf
Dead Load on Shelf - DL := 2.0 • psf
Section Properties of Double Rivet 'L' Post :
Modulus of Elasticity of Steel - E := 29000• ksi b := 1.5 in
h:= 1.5•in
Steel Yield Stress - F .= 33 • ksi • r 0.47•in
Section Modulus in x and y - 5 0.04.in r 0.47.in
x •_
Moment of Inertia in x and y - I := 0.06•in t := 0.075.in
Full Cross Sectional Area - A = 0.22•in h� := 1.42 in
b := 1.42•in
Length of Unbraced Post - L := 17.15.in L := 17.15•in i := 17.15•in
Effective Length Factor - K := 1.0 K r : 1.0 K := 1.0
Section Properties Continued:
Density of Steel - psteel := 490.pcf
Weight of Post - W := psteel•A W = 7.4861•Ib
Vertical DL on Post - Pd := DL•w•.25d•N + W Pd = 47.4861lb
Vertical LL on Post - PI := LL•w•.25•d•N P1= 100lb
Total Vertical Load on Post - P, := P + Pi P = 147.4861.lb
1
Eclipse Engineering, Inc. True Religion Brand Jeans 11/25/2009
Engineer: Nick Burnam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE
Floor Load Calculations :
Weight of Mobile Carriage: W := 90•Ib
Total Load on Each Unit: W := 4.P + W W = 679.94441b
Area of Each Shelf Unit: A := w•d A„ = l0ft
Floor Load under Shelf: PSF := W •A„ PSF = 67.9944• psf
NOTE: ACCUMULATED SHELVING LIVE LOAD IS LESS THAN 100 psf & THEREFORE, ACCEPTABLE.
Find the Seismic Load using Full Design Live Load :
ASCE -7 Seismic Design Procedure:
Importance Factor - IE := 1.0
Determine S and S from maps - S := 0.947 S 0.341
Determine the Site Class - Class D
Determine F and F - F := 1.121 F„ := 1.719
• Determine S and SM1 _ SMS := Fa•Ss SM1:= Fv•S1
SMS = 1.0616 SM1 = 0.5862
Determine SOS and SDI _ SDs := 3 • MS SDI := 3 •
SOS = 0.708 SDI = 0.391
Structural System - Section 15.5.3 ASCE -7:
4. Steel Storage Racks R := 4.0 n := 2 Cd := 3.5
R := R a p • = 2.5 I := 1.0
Total Vertical LL Load on Shelf - W LL•w•d Wi = 501b
W Vertical DL Load on Shelf - Wd := DL•w•d + 4.— N p Wd = 23.7431 lb
Seismic Analysis Procedure per ASCE -7 Section 13.3.1:
Average Roof Height - h := 20.0•ft
Height of Rack Attachment - z := 0.00•ft (0' -0" Used For Ground Floor Space)
0.4•a zl
Seismic Base Shear Factor - V := r 1 + 2• h l V = 0.1769
Rp
Shear Factor Boundaries - Vtm;n := 0.3•SDS•I Vtmin = 0.2123
Vtmax 1.6• I p Vtmax = 1.1324
V := if(V > Vtmax , Vtmax • Vt)
V := if (V < Vunin , Vtrnm , Vt) Vt = 0.212
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Eclipse Engineering, Inc. True Religion Brand Jeans 11/25/2009
Engineer: Nick Burnam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE
Seismic Loads Continued :
V ASD, Shear may be reduced - V := t V = 0.1517
1.4
Seismic DL Base Shear - Vtd := Vp • Wd • N Vtd = 28.811b
DL Force per Shelf : Fd := Vp • Wd Fd = 3.6 lb
Seismic LL Base Shear - Vtd := V • WI • N Vti = 60.66 lb
LL Force per Shelf : F1:= V • WI F1 = 7.58 lb
0.67 * LL Force per Shelf : FI.67 := 0.67•V • WI FI.67 = 5.08 lb
Force Distribution per ASCE -7 Section 15.5.3.3:
Operating Weight is one of Two Loading Conditions :
Condition #1: Each Shelf Loaded to 67% of Live Weight
Cumulative Heights of Shelves -
H := 0•S + 1.S+ 2.S + 3.S+ 4.S+ 5.S+ 6•S + 7•S
Total Moment at Shelf Base - M H•Wd + H•0.67•WI M = 2290.7ft•lb H = 40.02•ft
Vertical Distribution Factors for Each Shelf -
Total Base Shear - Vtotal := Vtd + 0.67•V Vtotal = 69.45 lb
Wd•0.0.5+ WI.0.67.0.0•S Wd•1.0•S+ WI.0.67.1.0•S
C1:= Mt C1= 0 C2: Mt C2 = 0.0357
F1 C1•(Vtotal) F1 = 0 F2 := C2•(Vtota1) F2 = 2.48 lb
Wd• 2.0.5+ WI.0.67.2.0•S Wd• 3.0•S+ WI.0.67.3.0•S
C3 := C3 = 0.0714 C4 := C4 = 0.1071
M M
F3 C3 . (Vtotal) F3 = 4.96Ib F4 := C4•(Vtotai) F4 = 7.441b
Wd•4.0•S+ WI.0.67.4.0.S Wd• 5.0.S+ WI.0.67.5.0•S
C5 := C5 = 0.1429 C6 = C6 = 0.1786
M M
F5 C5•(Vtotai) F5 = 9.92Ib F6 := C6•(Vtotal) F6 = 12.4Ib
Wd •6.0•S+ WI.0.67.6.0•S Wd •7.0•S+ W1.0.67.7.0.5
C7 := Mt C7 = 0.2143 C8 := C8 = 0.25
Mt
F7 := C7• (Vtotal) F7 = 14.88lb F8 := C8• F8 = 17.36 lb
Wd •8.0•S + W Wd •9.0•S + WI.0.67.9.0•S
C9 := Mt C = 0.2857 C10 := Mt C10 = 0.3214
Fg := Cg•(Vtotal) Fg= 19.84lb F10 = C1o•(Vtotai) F = 22.32 lb
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Eclipse Engineering, Inc. True Religion Brand Jeans 11/25/2009
Engineer: Nick Burnam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE
Wd•10.S+ W1.0.67- 10.S W W •
C M C = 0.3571 C12 := M C12 = 0.3929
t t
F11 C11•(Vtotai) F11 = 24.8 lb F12 := C12•(Vtotal) - F12 = 27.28 lb
CI +C2 +C3 +C4 +C5 +C6 + =1 V
•
Force Distribution Continued : Coefficients Should total 1.0
Condition #2: Top Shelf Only Loaded to 100% of Live Weight. .
Total Moment at Base of Shelf - M := 7.0•S•Wd + 7.0•S W Mm = 737.7ft•Ib
Total Base Shear - Vtotal2 Vtd + Fl . Vtotal2 = 36.39 lb ,
Wd•0.0•S+ 0•WI.0.0.S
C1a M Cia = 0 . Fla Cia•(Vtotal2) Fla = 0 -
ta
Wd .7.0 -S+ WI-7.0•S
Clia V M . Clia = 1 Fila C11a•(Vtotal2) Flu = 36.39 lb
V
Condition: #i Controls for Total Base Shear
By Inspection, Force Distribution for intermediate shelves without LL are negligible. .
Moment calculation for each column is based on total seismic base shear.
Column at center of rack is the worst case for this shelving rack system.
. Column Design .in Short Direction : M := 4 2 (Vm + v) M = 15.9831 ft- lb . .
.Bending Stress on Column - fbx := MSS, 1 fbx = 4.7949•ksi
Allowable Bending Stress- Fb := 0.6•F Fb = 19.8 -ksi
Bending at the Base of Each Column is Adequate .
Moment at Rivet Connection: , •
,
Shear on-each rivet - V. := V = 127.865lb -
1.5•in V
d := 0.25-in _
d
A := 4 A = 0.0491 • in
V r
Steel Stress on Rivet - f := f,; = 2.6062 • ksi
A
r
Allowable Stress on Rivet - F := 0.4.80 • ksi Fvr = 32 • ksi
RIVET CONNECTION IS ADEQUATE FOR MOMENT CONNECTION FROM BEAM TO POST
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Eclipse Engineering, Inc. True Religion Brand Jeans 11/25/2009
Engineer: Nick Bumam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE •
Find Allowable Axial Load for Column : •
Allowable Buckling.Stresses - - •
•
aex.x �2 E . (r = 214.9637. ksi
KX•Lx
r
Qex := vex,x v = 214.9637. ksi
•
- Distance from Shear Center ec t•hc2; bk2 e = 1.2706 in
to•CL of Web via X.axis 4 I •
Distance From CL Web to Centroid - x := 0.649-in — 0.5•t x = 0.6115•in
Distance From Shear Center x := x + e x = 1.8821 • in •
' to Centroid -
Polar Radius of Gyration - r Jr + r + xa r = 1:996•in
• — Torsion Constant -, 3:= 3 -(24;4 + h•t • J = 0.00063•in
•
Warping Constant- t•b Car P 9 := C = 0.0339•in
12 6•1)4 + h.t
•
Shear Modulus - G := 11300.ksi
1 7 r 2 E
• • v := • • G • ] + 2 Q = 45.7969 • ksi
Ap ro 2 ( Kt Lt�
•
L. 2
a := 1— — 3= 0.1109
•
',ro •
F := 1 •[(v + Qt) = J(a + vt) — 4 •a•vex•at] Fet = 38.3801•ksi.
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Elastic Flexural Buckling.Stress - F := if(F < v F v) F = 38.3801•ksi
Allowable Compressive Stress - F„ = F > 2 , F 1— 4.F , F F = 25.9065•ksi
e
Factor of Safety for Axial Comp. - 0 := 1.92
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• Eclipse Engineering, Inc. True Religion Brand Jeans • 11/25/2009
Engineer: Nick Burnam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE
Find Effective Area - •
Determine the Effective Width of Flange -
Flat width of Flange - wf := b — 0.54 wf =1.4625.in
Flange Plate Buckling Coefficient - kf := 0.43
w F
Flange Slenderness Factor - of
1. 052 f n of = 0.935
t E
0.22 1
•
pf Cl / . pf = 0.8179
l X f J X f
Effective Flange Width - b := if(a > 0.673, pf•wf, wf) b = 1:1961•in
Determine Effective Width of Web -
Flat width . of Web - V w := h — t V w = 1.425•in
Web Plate Buckling Coefficient - k., := 0.43 -
w E = 0
Web Slenderness Factor - � := 1 t E �w 0.911
pw C l 0.22 1 p = 0.8326 •
>w Xw
Effective Web Width - h := if(x,,, > 0.673, p , w h = 1.1864.in
Effective Column Area - A := t•(h + be) A = 0.1787• in
Nominal Column Capacity - P := A P = 4629lb
P n
Allowable Column Capacity - P := P = 2411 lb
- n
Check Combined Stresses - V •
'rt• 2 •E•I u
P P =6x 10 lb
-
(K
• Pa := Pax P = 58388Ib
,Magnification Factor - • no. Pp
a := 1 a = 0.9952 C := 0.85
Pa
' Combined Stress: V
?p + Cm•fbx = 0.268 ! MUST BE LESS THAN 1.0
Pa Fb.a
Final Design: 16ga 'L' POSTS WITH BEAM BRACKET ARE ADEQUATE FOR
REQD COMBINED AXIAL AND BENDING LOADS •
NOTE: P is the total vertical load on post, not 67% live load, so the design is conservative
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Eclipse Engineering, Inc. True Religion Brand Jeans 11/25/2009
• Engineer: Nick Burnam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE
•
STEEL STORAGE RACK DESIGN
PER 2006 IBC & 2007 CBC - 2208 & ASCE -7 SECTION 15.5.3
Find Overturning. Forces :
• . Total Height of Shelving Unit - H := 10.0•ft Width of Shelving Unit - w := 4.00.ft
Depth of Shelving Unit - d := 2.50.ft WORST CASE
_ Number of Shelves - N 8.0 Vertical Shelf Spacing - S := 17.15•1n
• Height to Top Shelf Center of G - h top := H h top = 10 ft
Height to Shelf Center of G - h :_ (N 2 1) •S h = 6.4312•ft
From Vertical Distribution of Seismic Force previously calculated -
` Controlling Load Cases -
Weight of Rack and 67 of LL - W :_ (W + 0.67•Wi)•N W = 457.94441b
• Seismic Rack and 67% of LL - V := Vtd + 0.67•Vn V = 69.4497lb
Ma := F + F + F + F + F + F6.5•S + F F
M : Ma
Overturning Rack and 67% of LL - M = 496.3ft•Ib
Weight of Rack and 100% Top Shelf - W :• Wd N + W1 W = 239.94441b
Seismic Rack and 100% Top Shelf - V := Vtd + FI V = 36.3888 lb .
Overturning Rack and 100% Top Shelf - M := Vtd he + F h top M = 261.1 ft•lb .
Controlling Weight - W := if(W > W , W, W W = 457.944lb
Controlling Shear - V := if(V > V V, V Vc = 69.45 lb
. Controlling Moment - M := if(M > M M , M M = 496.28ft•Ib
Tension Force on Column Anchor - T := d� — 0.60.2` T = 61.13 lb
•
per side of shelving unit
T = if(T <0•Ib,0•Ib,T) T= 61.1271b
V Force on Column Anchor - V := 2 V = 34.7 lb
USE HILTI KWIK BOLT TZ ANCHOR (or equivalent) -
USE 3/8"4) x 2" embed installed per the requirements of Hilti
Allowable Tension Force - T := 915•Ib For 2500psi Concrete
Allowable Shear Force - V := 485•1b
i 1.0•T 1.0•V
Combined Loading - r T 1 + r V 1 = 0.138 MUST BE LESS THAN 1.33
a J 1 a
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Eclipse Engineering, Inc. True Religion Brand Jeans 11/25/2009
Engineer: Nick Bumam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE
STEEL ANIT -TIP CUP AND ANTI -TIP TRACK DESIGN •
Tension (Uplift) Force on each side T = 61.127051b V .
Connection from Shelf to Anti-Tip track: • , V
•
Capacity of 1/4" diameter bolt in 16 ga steel - -V Z.,:= 312•Ib •
if(T < 2.Z "(2)'1/4" Bolts are Adequate" , "No Good ") _ "(2) 1/4" Bolts are Adequate"
Use 3/16" Diameter anti-tip device
Yield Stress of Angle Steel - V F Y := 36•ksi . V
Thickness of Anti-tip Head - t := 0.090-in
Width of Anti-tip Rod + Radius - br := 0.25.in, V
Width of Anti-tip Head - ba = 0.490-in V •
•
b — b •
Width of Anti-tip Flange - L := 2 Le = 0.12.in
Tension Force per Flange leg - T 0.5•T T = 30.5635 lb
Bending Moment on Leg - M1:= T2La M = 0.152818•ft•Ib
•
• 2
•
Section Modulus of Leg - SI := ba 6 Si = 0.0007 in3
V MI
Bending Stress on Leg - f := fb = 2.7722 -ksii
•
f b V
Ratio of Allowable Loads - = 0.1027 MUST BE LESS THAN 1.00
0.75.F V
Width of Anti-Tip track - L := 5.1 . in
Thickness of Aluminum Track - t t := 0.25-in Average Thickness •
• Spacing of Bolts - Stb := 24 -in •
Ltt 2 •
Section Modulus of Track - St := 6 S = 0.0531•in V
T . Stb
Design Moment on Track - M :_ 8 M = 15.3 ft-lb
for continuous track section '
Bending Stress on Track - f := M = 3.4519 - ksi •
at'
Allowable Stress of Aluminum - Fb := 21•ksi
ANTI - CLIP STEEL CONNECTION AND TRACK ARE ADEQUATE
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Eclipse Engineering, Inc. True Religion Brand Jeans 11 /25/2009
• Engineer: Nick Bumam, PE
Consulting Engineers PORTLAND, OREGON Template: Rolf Armstrong, PE
Connection from Steel Racks to Wall
Ib
Seismic Analysis Procedure per ASCE -7 Section 13.3.1: p '=
Average Roof Height - h = 20ft
Height of Rack Attachments - zb := z + 10.ft zb = 10ft At Top for fixed racks
connected to walls
0.4.a zb
Seismic Base Shear Factor - V := 1 + 2•— V = 0.3539 •
Rp h
•
Shear Factor Boundaries - Vtmin := 0.3•Sps•I V tmin = 0.2123. •
Vtmax 1.6• 5DS•I p Vtmax = 1.1324
V := if(Vt > Vtmax , Vtmax , Vt)
Vt := if(V < Vtmin , Vtmin • Vt) Vt = 0.354 .
• Seismic Coefficient - , V = 0.3539
Number of Shelves - N = 8 .
Weight per Shelf - Wtt := 50•Ib •
• Total Weight on Rack - WT := 4•P WT = 589.94441b
0.7•Vt-WT
Seismic Force at top and bottom - T„ := 2 T = 73.0657lb
• Connection at Top:
Standard Stud Spacing - Stuud := 16•in
Width of Rack - w = 4ft
• Number of Connection Points N := floor(w J N = 3
on each rack - . l Sstud J
Force on each connection F := - F = 24.3552lb
point - Nc
•
Capadty per inch of W := 135 - Ib
embedment - in
F
Required Embedment - d := W ' d = 0.1804• in
For Steel Studs - e
Pullout Capacity in 20 ga studs T20 := 83•Ib For #10 Screw - LARR #25294
LARR #25670
MIN #10 SCREW ATTACHED TO WALL IS ADEQUATE TO RESIST
SEISMIC FORCES ON SHELVING UNITS. EXPANSION BOLT IS.
ADEQUATE, BY INSPECTION, FOR THE BASE CONNECTION
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Conterminous 48 States
2005 ASCE 7 Standard •
Latitude = 45.45 "
Longitude = - 122.78194
Spectral Response Accelerations Ss and S1 •
Ss and S1 = Mapped Spectral Acceleration Values •
Site Class B- Fa= 1.0,Fv= 1.0
Data are based on a 0.05000000074505806 -deg grid spacing
•
Period Sa. •
(sec) (g) .
0.2 0.947 (Ss, Site Class B) •
1.0 0.341 (S1, Site Class B) . "
•
Conterminous 48 States
2005 ASCE 7 Standard •
Latitude = 45.45 •
Longitude = - 122.78194
Spectral Response Accelerations SMs and SM1 •
SMs =Fax Ss and SM1 =FvxS1
Site Class D - Fa = 1.121 ,Fv = 1.719
Period Sa
(sec) (g) • •
0.2 1.062 (SMs, Site Class D) •
1.0 0.585 (SM1, Site Class D)
Conterminous 48 States
2005 ASCE 7 Standard
Latitude = 45.45 •
•
Longitude = - 122.78194 •
. Design Spectral Response Accelerations S Ds and SD1 -
SDs = 2 /3x SMs and SD1 = 2/3 x SM1
Site Class D - Fa = 1.121 ,Fv = 1.719
Period Sa
(sec) (g)
0.2 0.708 (SDs, Site Class D)
1.0 0.390 (SD1, Site Class D)
Page 11 of 14 ESR -1917
TABLE 9 -KB -TZ CARBON AND STAINLESS STEEL ALLOWABLE SEISMIC TENSION (ASD), NORMAL - WEIGHT
CRACKED CONCRETE, CONDITION B (pounds)' _
Concrete Compressive Strength
Nominal Embedment f c = 2,500 psi Pc = 3,000 psI Pc = 4,000 psi f c = 8,000 psI
Anchor Depth her
• Diameter (In.) Carbon Stainless Carbon Stainless Carbon Stainless Carbon Stainless
steel steel steel steel steel steel steel steel
3/8 2 1,006 1,037 1,102 1,136 1,273 1,312 1,559 1,607
1/2 2 1,065 1,212 1,167 1,328 1,348 1,533 1,651 1,878
31/4 2,178 2,207 2,386 2,418 2,755 2,792 3,375 3,419
5/8 31/8 2,081 2,081 2,280 2,280 2,632 2,632 3,224 3,224
4 3,014 2,588 3,301 2,835 3,812 3,274 4,669 4,010
3 3/4 2,736 3,594 2,997 3,937 3,460 4,546 4,238 5,568
3/4
4 3/4 3,900 3,900 4,272 4,272 4,933 4,933 6,042 6,042
For SI: 1 Ibf = 4.45 N, 1 psi = 0.00669 MPa For pound -inch wits: 1 mm = 0.03937 Inches
'Values are for single anchors with no edge distance or spacing reduction. For other cases, calculation of Rd as per ACI 318-05 and conversion
to ASD in accordance with Section 4.2.1 Eq. (5) is required.
2 Values are for normal weight concrete. For sand - lightweight concrete, multiply values by 0.60.
2 Condition B applies where supplementary reinforcement in conformance with ACI 318-05 Section D.4.4 is not provided, or where pullout or
pryout strength governs. For cases where the presence of supplementary reinforcement can be verified, the strength reduction factors
associated with Condition A may be used.
TABLE 10 -KB-TZ CARBON AND STAINLESS
STEEL ALLOWABLE SEISMIC SHEAR LOAD (ASD),
(pounds)'
Nominal Allowable Steel Capacfty, Seismic Shear
Anchor
Diameter Carbon Steel Stainless Steel
3/8 999 1,252
1/2 2,839 3,049
5/8 4,678 5,245
3/4 6,313 6,477
For SI: 1 lbf = 4.45 N
'Values are for single anchors with no edge distance or
spacing reduction due to concrete failure.