steel base plate design

"BASEPLT9" --- STEEL COLUMN BASE PLATE ANALYSIS

Program Description:

"BASEPLT9" is a spreadsheet program written in MS-Excel for the purpose of analysis of steel column base

plates. Specifically, wide flange column base plates may be subjected to axial loads (compression or tension),

with or without major-axis column bending, plus major-axis shear. Base plate bearing pressure is checked as

well as bolt tension, if applicable. If shear is present, bolt shear as well as interaction of bolt tension and shear,

if applicable, are calculated. Finally, the required base plate thickness is calculated. There is a separate

worksheet for base plate shear lug design, when shear load is high and cannot be effectively handled by bolts.

This program is a workbook consisting of four (4) worksheets, described as follows:

Worksheet Name DescriptionDoc This documentation sheet

Base Plate Steel column base plate analysis

Shear Lug Steel column base - shear lug analysis

Base Plate (Table) Multiple steel column base plate analysis (table format)

Program Assumptions and Limitations:

1. This program follows the procedures and guidelines of the AISC 9th Edition Allowable Stress (ASD) Manual

(2nd Revision, 1995) for wide flange column base plates subjected to axial compressive load only.

2. This program uses a "cubic equation" method of solution for column base plates subjected to axial

compression or tension load with major axis column bending as presented in the reference:

"Design of Welded Structures" - by Omer W. Blodgett (James F. Lincoln Arc Welding Foundation)

3. For interaction of anchor bolt tension and shear, this program follows the article:

"Design Aid: Anchor Bolt Interaction of Shear and Tension Loads", by Mario N. Scacco

AISC Engineering Journal, 4th Quarter - 1992.

4. User has option to take out some of the total shear though friction between column base and grout based

on column dead load and coefficient of friction, thus reducing amount of shear to be taken by anchor bolts.

5. This program uses the database of member dimensions and section properties from the "AISC Shapes

Database", Version 3.0 (2001) as well as the AISC 9th Edition (ASD) Manual (1989).

6. This program assumes that the base plate is sufficiently rigid to assume linear distribution of load to the

base plate and/or anchor bolts. (Note: adequate base plate rigidity is most likely assured if the distance

from the face of the column to the edge of the base plate is <= 4*tp. See "General Anchorage to Concrete",

TVA Civil Design Standard DS-C1.7.1 (Rev. 1984), page 25.)

7. Additional assumptions used in this program are as follows:

a. The column is centered on the base plate in both directions.

b. Axial column load, 'P', can be = 0 for the case with moment.

c. The minimum area of concrete support is: A2(min) = N*B.

d. For a base plate supported on a slab or mat, use A2 = 4*(N*B).

e. Two (2) total rows of anchor bolts are allowed, one row outside of each column flange.

f. There must be an equal number of anchor bolts in each of the two (2) rows.

8. For cases with anchor bolt tension and base plate bearing, this program calculates the bending moment in

the base plate at two locations. One, at the column flange in compression using the bearing pressure

distribution, and the other at the column flange in tension using the tension in one bolt distributed over an

assumed width effective plate width based on edge distances and bolt spacing. At both locations, the

moment and resulting base plate thickness are calculated using a "cantilever" length equal to the calculated

"m" distance from the AISC code. Then, the larger of the two calculated thickness values is used for the

required base plate thickness. (Note: this program assumes that the anchor bolts are not located in plan

significantly beyond the ends of the column flange, so that corner-type plate bending does not control.)

9. The "Shear Lug" worksheet follows the AISC "Steel Design Guide Series #7 - Industrial Buildings - Roofs to

Column Anchorage" (page 33 and pages 38-40).

10. The "Base Plate (Table)" worksheet enables the user to analyze/design virtually any number of individual

column bases or column load combinations. Refer to that worksheet for list of specific assumptions used.

11. 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".)

"BASEPLT9.xls" ProgramVersion 3.7

3 of 7 04/18/2023 11:02:10

STEEL COLUMN BASE PLATE ANALYSISPer AISC 9th Edition Manual (ASD) and "Design of Welded Structures" (O. Blodgett)

For Axial Load with or without MomentJob Name: Subject: ###

Job Number: Originator: Checker: ######

Input Data: ######

Column Size: Column Properties: ###Select: W14x90 A = 26.50 in.^2

Column Loadings: d = 14.000 in. ###-130.00 kips tw = 0.440 in. ###

0.00 kips bf = 14.500 in. ###10.00 kips tf = 0.710 in. ###

Moment @ Base, M = 175.00 ft.-kips ###Design Parameters: ###

Base Plate Length, N = 28.750 in. ED1=2.5 ###Base Plate Width, B = 24.000 in. ###

Plate Yield Stress, Fy = 36.00 ksi ED2=2.5 n=6.2Concrete Strength, f 'c = 3.000 ksi. ###

1296.00 in.^2 ###Shear Coef., C = 1.85 B=24 0.80*bf

0.70 ###Anchor Bolt/Rod Data: ###

Total No. of Bolts, Nb = 6 n=6.2Bolt Diameter, db = 1.750 in. ###

Anchor Bolt Material = F1554 (36) m=7.73 0.95*d m=7.73 ###2.500 in. ###2.500 in. N=28.75 ###

###Results: ###

###Eccentricity, Bearing Length, and Bearing Pressures: e = M*12/P = 16.154 A307

Eccentricity, e = 16.154 in. A36Length, Xc = 15.532 in.

Fp = 1.439 ksi -1300.928 ksi (-down)

0.000 ksi F1554 (55)Fp >= fp(max), O.K. W14x90 Col. F1554 (105)

Anchor Bolt/Rod Tension and Shear: ###Ft = 19.10 ksi ###

Ta = 45.94 k/bolt tp=2.265Tb = 14.30 k/bolt ###

Ta >= Tb, O.K. fp(max)=0.928Fv = 9.90 ksi T= Xc=15.532 ###Va = 23.81 k/bolt Tb*(Nb/2) W40x174

10.00 N=28.75 W40x167Vb = 1.67 k/bolt W40x149

Va >= Vb, O.K. W36x848(Interaction) S.R. = 0.441 = Tb/Ta+(C*Vb)/Va W36x798

S.R. <= 1.0, O.K. W36x720Base Plate Thickness: Suggested plate thickness for rigidity:W36x650

2.265 in. 1.931 in. tp(min) >= max. of m/4 or n/4 W36x588

Axial Load, P(total) =Axial Load, P(DL) =

Shear Load, V(total) =

Bearing Area, A2 =

Coef. of Friction, m =

Bolt Edge Dist., ED1 =Bolt Edge Dist., ED2 =

Plan

P(total) =

fp(max) =fp(min) =

V(bolts) = = V(total)-1/2*m*P(DL)

Elevation

tp(req'd) = tp(min) =

be

C12

'P' is the axial load at the base of the column. Sign convention is as follows: tension (uplift) load = positive (+) compression (downward) load = negative (-)

C13

Note: if the user does not wish to consider friction between column base and grout to take a portion of the appled shear load, V(total), then input P(DL) = 0. Considering friction will reduce the shear to be taken by bolts. Sign convention: P(DL) = -down. Note: in the value of P(DL) to be input, the user may elect to also include ONLY the portion of column axial live load which produces shear, if any.

C14

'V' is the horizontal shear load at the base of the column, normally taken parallel to the web of the column or in 'N' direction of the base plate. However, user may input the vector sum of the simultaneous shear loads as: Vr = SQRT(Vx^2+Vy^2)

C15

The moment at the base of the column, 'M', is assumed to be about the X-axis of the column.

C17

The base plate length, 'N', is the length of the base plate parallel to the web (Y-axis) of the column.

C18

The base plate length, 'B', is the length of the base plate parallel to the flanges (X-axis) of the column.

C21

The total bearing area of the concrete support, 'A2', MUST have a minimum value of A2 = N*B. For base plates supported on slabs or mats, use A2 = 4*(N*B).

C22

Shear Coefficient, 'C': C = 1.85 for base plate on top of grout bed. C = 1.25 for base plate recessed in grout. C = 1.10 for base plate embedded in concrete. Reference: "Design of Headed Anchor Bolts" by John G. Shipp and Edward R. Haninger AISC Engineering Journal, 2nd Quarter - 1983.

C23

Coefficient of Friction,'m: m = 0.55 for base plate on top of grout bed. m = 0.70 for base plate recessed in grout. m = 0.90 for base plate embedded in concrete. Reference: AISC "Steel Design Guide Series #1 - Column Base Plates"

C25

'Nb' is the total number of anchor bolts on both sides of the column flanges. Note: anchor bolts MUST be in only 2 rows, one row outside of each column flange.

C28

ANCHOR BOLT DATA Bolt Dia. (db) Oversized Hole Dia. (dh) Min. Edge Distance (ED) 3/8" 11/16" 13/16" 1/2" 13/16" 15/16" 5/8" 15/16" 1-1/16" 3/4" 1-1/16" 1-3/16" 7/8" 1-3/16" 1-5/16" 1" 1-1/2" 1-1/2" 1-1/8" 1-5/8" 1-3/4" 1-1/4" 1-3/4" 1-7/8" 1-3/8" 1-7/8" 2" 1-1/2" 2" 2-1/4" 1-3/4" 2-1/4" 2-7/16" 2" 2-1/2" 2-3/4" 2-1/4" 3-1/4" 3-5/16" 2-1/2" 3-1/2" 3-5/8" 2-3/4" 3-3/4" 3-15/16" 3" 4" 4-1/4" Note: Minimum edge distances shown above are for base plates with either rolled, gas-cut, or saw-cut edges only.

C29


C34

The eccentricity (e) is: e = ABS(M*12/P)

C35

Note: P = -P (which was input) for use in equations below. For case of axial compression load plus moment: when: ABS(e) = M*12/P > N/2-Xc/3 MR = Es/Ec = 29000/(57*SQRT(f'c*1000)) , As = (Nb/2)*p*db^2/4 Xc^3 + 3*(e-N/2)*Xc^2 + 6*MR*As/B*((N/2-ED1)+e)*Xc - 6*MR*As/B*(N/2+(N/2-ED1))*((N/2-ED1)+e) = 0 Solve cubic equation for Xc when: N/6 < ABS(e) <= N/2-Xc/3 Xc = 3*(N/2-e) when: ABS(e) <= N/6 Xc = N For case of axial tension load plus moment: when: ABS(e) = M*12/P > N/2-ED1 MR = Es/Ec = 29000/(57*SQRT(f'c*1000)) , As = (Nb/2)*p*db^2/4 Xc^3 + 3*(e-N/2)*Xc^2 + 6*MR*As/B*((N/2-ED1)+e)*Xc - 6*MR*As/B*(N/2+(N/2-ED1))*((N/2-ED1)+e) = 0 Solve cubic equation for Xc when: ABS(e) <= N/2-ED1 Xc = 0

C36

Allowable concrete bearing stress, 'Fp', is determined as follows: for bearing on entire area of concrete support, Fp = 0.35*f'c for bearing on less than entire area of concrete support, Fp = 0.35*f'c*SQRT(A2/A1) <= 0.70*f'c where: A2 = Lpx*Lpy >= N*B A1 = N*B Note: the total bearing area of the concrete support, 'A2', MUST have a minimum value of A2 = N*B. For base plates supported on slabs or mats, use A2 = 4*(N*B).

C37

Note: P = -P (which was input) for use in equations below. For case of axial compression load without moment: fp(max) = fp(min) = fp = P/(N*B) For case of axial compression load plus moment: when: ABS(e) = M*12/P > N/2-Xc/3 T = -P*(N/2-Xc/3-e)/(N/2-Xc/3+(N/2-ED1)) , Tb = T/(Nb/2) fp(max) = 2*(P+T)/(Xc*B) when: N/6 < ABS(e) <= N/2-Xc/3 fp(max) = 2*P/(Xc*B) when: ABS(e) <= N/6 fp(max) = ABS(P)/(N*B)*(1+6*e/N) For case of axial tension load plus moment: when: ABS(e) = M*12/P > N/2-ED1 Tb = -P*(N/2-ED1-M*12/P)/(2*(N/2-ED1))/(Nb/2) T = Tb*(Nb/2) fp(max) = 2*(P+T)/(Xc*B) when: ABS(e) <= N/2-ED1 fp(max) = 0

C41

Allowable Tension Stress (Ft) on Anchor Bolts Description of Anchor Bolts Ft (ksi) Fu (ksi) Fy( ksi) A307 bolts 20.0 60.0 36.0 A36 threaded rods 19.1 58.0 36.0 A572 threaded rods 21.5 65.0 50.0 A588 threaded rods 23.1 70.0 50.0 F1554 (Gr.36) th'd. rods 19.1 58.0 36.0 F1554 (Gr.55) th'd. rods 24.8 75.0 55.0 F1554 (Gr.105) th'd. rods 41.3 125.0 105.0 Note: Ft = 0.33*Fu

C42

Anchor Bolt Data Nominal Diameter, db (in.) Area, Ab (in.^2) Allowable Tension, Ta (kips) A307 A36 A572 A588 F1554 (36) F1554 (55) F1554 (105) 3/8 0.1104 2.21 2.11 2.37 2.55 2.11 2.74 4.56 1/2 0.1963 3.93 3.75 4.22 4.53 3.75 4.87 8.11 5/8 0.3068 6.14 5.86 6.60 7.09 5.86 7.61 12.67 3/4 0.4418 8.84 8.44 9.50 10.21 8.84 10.96 18.25 7/8 0.6013 12.03 11.48 12.93 13.89 11.48 14.91 24.83 1 0.7854 15.71 15.00 16.89 18.14 15.00 19.48 32.44 1-1/8 0.9940 19.88 18.98 21.37 22.96 18.98 24.65 41.05 1-1/4 1.2272 24.54 23.44 26.38 28.35 23.44 30.43 50.68 1-3/8 1.4850 29.70 28.36 31.93 34.30 28.36 36.83 61.33 1-1/2 1.7671 35.34 33.75 37.99 40.82 33.75 43.82 72.98 1-3/4 2.4053 48.11 45.94 51.71 55.56 45.94 59.65 99.34 2 3.1416 62.83 60.00 67.54 72.57 60.00 77.91 129.75 2-1/4 3.9761 79.50 75.94 85.49 91.85 75.94 98.61 164.21 2-1/2 4.9087 98.17 93.76 105.54 113.39 93.76 121.74 202.73 2-3/4 5.9396 118.79 113.45 127.70 137.20 113.45 147.30 245.31 3 7.0686 141.37 135.01 151.97 163.28 135.01 175.30 291.93 Note: allowable tension values are for no shear.

C43

Note: P = -P (which was input) for use in equations below. For case of axial compression load plus moment: when: ABS(e) = M*12/P > N/2-Xc/3 , Tb > 0 T = -P*(N/2-Xc/3-e)/(N/2-Xc/3+(N/2-ED1)) Tb = T/(Nb/2) when: ABS(e) <= N/2-Xc/3 Tb = 0 For case of axial tension load plus moment: when: ABS(e) > N/2-ED1: Tb = -P*(N/2-Xc/3-M*12/P)/(N/2-Xc/3+(N/2-ED1))/(Nb/2) when: ABS(e) <= N/2-ED1: Tb = -P*(N/2-ED1-M*12/P)/(2*(N/2-ED1))/(Nb/2)

C45

Allowable Shear Stress (Fv) on Anchor Bolts Description of Anchor Bolts Fv (ksi) Fu (ksi) A307 bolts 10.0 60.0 A36 threaded rods 9.9 58.0 A572 threaded rods 11.1 65.0 A588 threaded rods 11.9 70.0 F1554 (Gr.36) th'd. rods 9.9 58.0 F1554 (Gr.55) th'd. rods 12.8 75.0 F1554 (Gr.105) th'd. rods 21.3 125.0 Note: Fv = 0.17*Fu (for threads included in shear plane).

C46

Anchor Bolt Data Nominal Diameter, db (in.) Area, Ab (in.^2) Allowable Shear, Va (kips) A307 A36 A572 A588 F1554 (36) F1554 (55) F1554 (105) 3/8 0.1104 1.10 1.09 1.23 1.31 1.09 1.41 2.35 1/2 0.1963 1.96 1.94 2.18 2.34 1.94 2.51 4.18 5/8 0.3068 3.07 3.04 3.41 3.65 3.04 3.93 6.53 3/4 0.4418 4.42 4.37 4.90 5.26 4.37 5.66 9.41 7/8 0.6013 6.01 5.95 6.67 7.16 5.95 7.70 12.81 1 0.7854 7.85 7.78 8.72 9.35 7.78 10.05 16.73 1-1/8 0.9940 9.94 9.84 11.03 11.83 9.84 12.72 21.17 1-1/4 1.2272 12.27 12.15 13.62 14.60 12.15 15.71 26.14 1-3/8 1.4850 14.85 14.70 16.48 17.67 14.70 19.01 31.63 1-1/2 1.7671 17.67 17.49 19.62 21.03 17.49 22.62 37.64 1-3/4 2.4053 24.05 23.81 26.70 28.62 23.81 30.79 51.23 2 3.1416 31.42 31.10 34.87 37.38 31.10 40.21 66.92 2-1/4 3.9761 39.76 39.36 44.13 47.32 39.36 50.89 84.69 2-1/2 4.9087 49.09 48.60 54.49 58.41 48.60 62.83 104.56 2-3/4 5.9396 59.40 58.80 65.93 70.68 58.80 76.03 126.51 3 7.0686 70.69 69.98 78.46 84.12 69.98 90.48 150.56 Note: allowable shear values are for no tension.

C47

The actual shear to be taken by the anchor bolts with or without a portion taken out by friction between column base and grout, 'V(bolts)', is calculated as follows: V(bolts) = V(total)-1/2*m*P(DL)

C48

The actual bolt shear, 'Vb', is calculated as follows: Vb = V(bolts)/Nb where: V(bolts) = V(total)-1/2*m*P(DL)

C50

Stress ratio for interaction of combined anchor bolt tension and shear is calculated as follows: S.R. = Tb/Ta+(C*Vb)/Va <= 1.0 where: C = Shear Coefficient = 1.85 for base plate on top of grout bed = 1.25 for base plate recessed in grout = 1.10 for base plate embedded in concrete References: 1. "Design Aid: Anchor Bolt Interaction of Shear and Tension Loads" by Mario N. Scacco AISC Engineering Journal, 4th Quarter - 1992. 2. "Design of Headed Anchor Bolts" by John G. Shipp and Edward R. Haninger AISC Engineering Journal, 2nd Quarter - 1983.

C53

Note: P = -P (which was input) for use in equations below. For column base plates subjected to concentric axial compression load without moment: fp = P/(N*B) , m = (N-0.95*d)/2 , n = (B-0.8*bf)/2 , n' = SQRT(d*bf)/4 q = 4*fp*d*bf/((d+bf)^2*Fp) < 1.0 , l = 2*(1-SQRT(1-q))/SQRT(q) <= 1.0 tp = 2*c*SQRT(fp/Fy) , where: c = maximum of: m, n, or l*n' For column base plates subjected to axial load plus moment: If Xc > m , tp = maximum of: tp = SQRT(6*((fpmax-((fpmax-fpmin)/Xc)*m)*m^2/2+((fpmax-fpmin)/Xc)*m^3/3)/(0.75*Fy)) tp = 2*n*SQRT((fpmax+fpmin)/2/Fy) tp = 2*(l*n')*SQRT((fpmax+fpmin)/2/Fy) tp = SQRT(6*Tb*(m-ED1)/be/(0.75*Fy)) If Xc <= m , tp = maximum of: tp = SQRT(6*fpmax*Xc/2*(m-Xc/3)/(0.75*Fy)) tp = SQRT(6*Tb*(m-ED1)/be/(0.75*Fy)) where: be = min. of: (m-ED1) or (B-2*ED2)/(2*(Nb/2-1)) + min. of: (m-ED1) or (B-2*ED2)/(2*(Nb/2-1)) or ED2

F53

Adequate base plate rigidity is most likely assured if the distance from the face of the column to the edge of the base plate is <= 4*tp. See "General Anchorage to Concrete", TVA Civil Design Standard DS-C1.7.1 (Rev. 1984), page 25.) Thus, suggested minimum base plate thickness to ensure assumption of plate rigidity is as follows: tp(min) >= maximum of: m/4 or n/4 where: m = (N-0.95*d)/2 n = (B-0.80*bf)/2


4 of 7 04/18/2023 11:02:10

W36x527


5 of 7 04/18/2023 11:02:10

STEEL COLUMN BASE - SHEAR LUG ANALYSISPer AISC 9th Edition Manual (ASD), AISC "Steel Design Guide Series No. 1"

and AC1 318-99 CodeJob Name: Subject: ###

Job Number: Originator: Checker: ######

Input Data: ######

Column Loadings: ###17.25 kips ###0.00 kips ( - = down) P(DL)=0 ###

###Base and Shear Lug Data: Column ###

Base Plate Length, N = 14.000 in. ###Base Plate Width, B = 14.000 in. ###Base Plate Thk., tp = 1.5000 in. V=17.25 EDx =Grout Thickness, G = 2.00 in. tp=1.5

Lug Height, H = 4.00 in. G=2Lug Width, W = 9.00 in. Grout H=4

Lug Thickness, t = 1.250 in. w0.3125 in. Shear Lug s =

Lug Yield Stress, Fy = 36.00 ksi t=1.25 Rw =0.55

Pier Length, Lpx = 20.000 in.

Pier Width, Lpy = 20.000 in.

Concrete Strength, f 'c = 3.000 ksi

Results:

Shear Lug Design Loads:Shear, V(lg) = 17.25 kips

Moment, M(lg) = 5.75 in-kips/in. M(lg) = (V(lg)/W)*(H+G)/2

Shear Lug Thickness:1.130 in. t(req'd) = SQRT(6*M(lg)/(0.75*Fy)) <= t <= tp

t(req'd) <= t, O.K.Concrete Bearing at Lug:

fp = 0.958 ksi fp = V/(W*(H-G))Fp = 1.050 ksi Fp = 0.35*(f'c) Fp >= fp, O.K.

Concrete Shear in Front of Lug:Vu = 29.33 kips Vu = 1.7*V(lg) (assume L.F. = 1.7)

EDx = 9.375 in. EDx =(Lpx-t)/2EDy = 5.500 in. EDy =(Lpy-W)/2

Av = 209.50 in.^2 Av = (2*EDy+W)*(H-G+EDx)-(H-G)*W39.01 kips

Vu <= V(allow), O.K.Shear Lug Welding:

s = 1.458 in.

Rw = 4.058 k/in. Rw = SQRT((M(lg)/s)^2+(V(lg)/(2*W))^2)0.273 in. Weld >= req'd., O.K.

Shear Load, V(total) =Axial Load, P(DL) =

fVc =

Weld Size, w =

Coef. of Friction, m = w(req'd) =

Nomenclature

V(lg) = V-1/2*m*ABS(P(DL))

t(req'd) =

fVc = fVc = 4*0.85*SQRT(f'c*1000)/1000*Av (allowable)

s = t+2*(1/3)*w (moment arm between C.G. of welds)

w(req'd) = w(req'd) = Rw/(0.7071*0.3*70)

C11

Note: if the user does not wish to consider friction between column base and grout to take a portion of the appled shear load, V(total), then input P(DL) = 0. Considering friction will reduce the shear to be taken by lug. Sign convention: P(DL) = -down. Note: in the value of P(DL) to be input, the user may elect to also include ONLY the portion of column axial live load which produces shear, if any.

C14


C15


C23

Coefficient of Friction,'m: m = 0.55 for base plate on top of grout bed. m = 0.70 for base plate recessed in grout. m = 0.90 for base plate embedded in concrete.

I36

If t(req'd) > t, then increase shear lug thickness used (t), or reduce bending in lug by either decreasing grout depth (G) or lug height (H).

I39

If Fp < fp, then either decrease grout depth (G) or increase lug height (H) or lug width (W) , which may mean increasing the base plate width (B).

C45

The concrete design shear strength for the lug is determined based on a uniform tension stress of 4*0.85*SQRT(f'c) acting on an effective stress area defined by projecting a 45 degree plane from the bearing edge of the shear lug to the free surface of the pier. The effective (embedded) bearing area of the shear lug is to be excluded from the projected area.

I47

If Vb(allow) < Vu, then either decrease grout depth (G) or increase lug height (H) or lug width (W) , which may mean increasing the base plate width (B). Also, can increase pier dimensions (Lpx and Lpy).

I51

If weld size req'd. > weld size used, then increase shear lug thickness used (t), or reduce bending in lug by either decreasing grout depth (G) or lug height (H).


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7 of 7 04/18/2023 11:02:10

STEEL COLUMN BASE PLATE ANALYSISPer AISC 9th Edition Manual (ASD) and "Design of Welded Structures" (O. Blodgett) Program follows the procedures and guidelines of the AISC 9th Edition Allowable Stress (ASD) Manual (2nd Revision, 1995) pages 3-106 to 3-110 for wide

For Axial Load with or without Moment flange column base plates subjected to concentric axial compressive load only.Job Name: Subject: 2. Program uses a "cubic equation" method of solution for column base plates subjected to axial compression or tension load with major axis column bending

Job Number: Originator: Checker: e = M*12/P as presented in "Design of Welded Structures" - by Omer W. Blodgett (James F. Lincoln Arc Welding Foundation), pages 3.3-6 to 3.3-10.3. The total number of anchor bolts on both sides of the column flanges is 'Nb'. Anchor bolts MUST be in only 2 rows, one row outside of each column flange.

Input Data: ED1 4. Permitted anchor bolt diameters are: 3/8", 1/2", 5/8", 3/4", 7/8", 1", 1-1/8", 1-1/4", 1-3/8", 1-1/2", 1-3/4", 2", 2-1/4", 2, 1/2", 2-3/4", and 3".P 5. For case of concentric axial compression load without moment:

Base Plate Yield Stress, Fy = 50.00 ksi n (-down) P = -P (which was input) for use in equations belowConcrete Compressive Strength, f'c = 3.000 ksi

Anchor Bolt/Rod Material = F1554 (36) Col.Shear Coefficient, C = 1.85 B 0.80*bf 6. For case of axial load (compression or tension) plus moment resulting in anchor bolt tension, with eccentricites (e) as shown below:

P = -P (which was input) for use in equations below

tp ABS(e) = M*12/P > N/2-Xc/3 (for P = compression) , ABS(e) = M*12/P > N/2-ED1 (for P = tension)n MR = Es/Ec = 29000/(57*SQRT(f'c*1000)) , As = (Nb/2)*p*db^2/4

fp(max) Xc^3 + 3*(e-N/2)*Xc^2 + 6*MR*As/B*((N/2-ED1)+e)*Xc - 6*MR*As/B*(N/2+(N/2-ED1))*((N/2-ED1)+e) = 0 , and solve cubic equation for Xc m 0.95*d m T= Xc T = -P*(N/2-Xc/3-e)/(N/2-Xc/3+(N/2-ED1)) , Tb = T/(Nb/2) , fp(max) = 2*(P+T)/(Xc*B)

Tb*(Nb/2) 7. Plate bending is calculated due to both plate bearing stress and anchor bolt tension, where effective plate width used for anchor bolt tension is as follows: N N be = Minimum of: (m-ED1) or (B-2*ED2)/(2*(Nb/2-1)) + Minimum of: (m-ED1) or (B-2*ED2)/(2*(Nb/2-1)) or ED2 (Note: Nb = either 2, 4, 6, or 8 bolts)

8. For interaction of anchor bolt tension and shear, this program follows the article: "Design Aid: Anchor Bolt Interaction of Shear and Tension Loads", by Mario N. Scacco, AISC Engineering Journal, 4th Quarter - 1992. Anchor bolt interaction formula is as follows: Tb/Ta + (C*Vb)/Va <= 1.0.

COLUMN LOADS DESIGN DATA RESULTSCOLUMN COLUMN Case 1: Maximum Load Condition Case 2: Minimum Load Condition Base Plate Data Pier Data Anchor Bolt Data Eccentricities and Bearing Lengths Bearing Pressure Check Plate Thk. Check Bolt Tension Check Bolt Shear Check Interaction

LOCATION SIZE Axial Shear Moment Axial Shear Moment Length Width Thickness Length Width Total No. Diameter Edge Dist. Edge Dist. Eccentricity Brg. Length Eccentricity Brg. Length fp(max) Fp S.R. = tp S.R. = Tb Ta S.R. = Vb Va S.R. = S.R. =P V M P V M N B tp Lpx Lpy Nb db ED1 ED2 (actual) (allowable) fp(max)/Fp (req'd) tp(req'd)/tp (actual) (allowable) Tb/Ta (actual) (allowable) Vb/Va Tb/Ta +

(kips) (kips) (ft-kips) (kips) (kips) (ft-kips) (in.) (in.) (in.) (in.) (in.) (in.) (in.) (in.) (in.) (in.) (in.) (in.) (ksi) (ksi) (in.) (kips) (kips) (kips) (kips) C*Vb/VaA-1 W10x100 -525.00 0.00 0.00 -525.00 0.00 0.00 19.000 17.000 2.000 28.000 28.000 4 1.000 1.500 1.500 0.000 19.000 0.000 19.000 1.625 1.636 0.994 1.579 0.790 0.00 15.00 0.000 0.00 7.78 0.000 ---A-2 W12x106 -600.00 0.00 0.00 -600.00 0.00 0.00 19.000 16.000 1.750 34.000 34.000 4 1.000 1.500 1.500 0.000 19.000 0.000 19.000 1.974 2.048 0.964 1.340 0.766 0.00 15.00 0.000 0.00 7.78 0.000 ---A-3 W10x100 -360.00 10.00 60.00 -360.00 10.00 60.00 19.000 17.000 2.000 36.000 36.000 4 1.250 2.000 2.000 2.000 19.000 2.000 19.000 1.818 2.100 0.866 1.565 0.783 0.00 23.44 0.000 2.50 12.15 0.206 ---A-4 W14x90 -130.00 10.00 59.58 -130.00 10.00 59.58 28.750 24.000 1.750 36.000 36.000 4 1.250 2.000 2.000 5.500 26.641 5.500 26.641 0.407 1.439 0.283 1.324 0.757 0.02 23.44 0.001 2.50 12.15 0.206 0.381A-5 W14x90 -130.00 10.00 175.00 -130.00 10.00 175.00 28.750 24.000 2.500 36.000 36.000 6 1.750 2.500 2.500 16.154 15.532 16.154 15.532 0.928 1.439 0.645 1.922 0.769 14.30 45.94 0.311 1.67 23.81 0.070 0.441A-6 W14x90 0.00 10.00 175.00 0.00 10.00 175.00 28.750 24.000 2.250 36.000 36.000 6 2.000 2.750 2.750 (Infinite) 10.602 (Infinite) 10.602 0.735 1.439 0.511 1.834 0.815 31.16 60.00 0.519 1.67 31.10 0.054 0.618A-7 W14x90 150.00 0.00 0.00 150.00 0.00 0.00 28.750 24.000 2.250 36.000 36.000 6 1.375 2.000 2.000 0.000 0.000 0.000 0.000 0.000 1.439 0.000 1.809 0.804 25.00 28.36 0.881 0.00 14.70 0.000 ---A-8 W14x90 150.00 5.00 50.00 150.00 5.00 50.00 28.750 24.000 2.500 36.000 36.000 6 1.750 2.500 2.500 4.000 0.000 4.000 0.000 0.000 1.439 0.000 1.963 0.785 33.42 45.94 0.727 0.83 23.81 0.035 0.792A-9 W14x90 130.00 10.00 175.00 130.00 10.00 175.00 28.750 24.000 2.750 36.000 36.000 6 2.250 3.500 3.500 16.154 5.762 16.154 5.762 0.425 1.439 0.296 2.156 0.784 53.14 75.94 0.700 1.67 39.36 0.042 0.778

Assumptions: 1.

fp = P/(N*B) , m = (N-0.95*d)/2 , n = (B-0.8*bf)/2 , n' = SQRT(d*bf)/4 , q = 4*fp*d*bf/((d+bf)^2*Fp) < 1.0 , l = 2*(1-SQRT(1-q))/SQRT(q) <= 1.0 tp = 2*c*SQRT(fp/Fy) , where: c = maximum of: m, n, or l*n'

Plan Elevation

e(case 1) Xc(case 1) e(case 2) Xc(case 2)

beED2

D391

Shear Coefficient, 'C': C = 1.85 for base plate on top of grout bed. C = 1.25 for base plate recessed in grout. C = 1.10 for base plate embedded in concrete. Reference: "Design of Headed Anchor Bolts" by John G. Shipp and Edward R. Haninger AISC Engineering Journal, 2nd Quarter - 1983.

C404


D404

'V' is the horizontal shear load at the base of the column, normally taken parallel to the web of the column or in 'N' direction of the base plate. However, user may input the vector sum of the simultaneous shear loads as: Vr = SQRT(Vx^2+Vy^2) Note: the user may wish to consider friction between column base and grout to take a portion of appled shear load, V, thus reducing the shear to be taken by bolts. The total shear to be taken by bolts, 'Vb(bolts)', is then calculated as follows: V(bolts) = V-1/2*m*P(DL) where: m = Coefficient of Friction = 0.55 for base plate on top of grout bed = 0.70 for base plate recessed in grout = 0.90 for base plate embedded in concrete P(DL) = portion of column load as dead load Note: in the value of column dead load, 'P(DL)', user may elect to also include ONLY the portion of column axial live load which produces shear, if any.

E404


F404


G404

'V' is the horizontal shear load at the base of the column, normally taken parallel to the web of the column or in 'N' direction of the base plate. However, user may input the vector sum of the simultaneous shear loads as: Vr = SQRT(Vx^2+Vy^2) Note: the user may wish to consider friction between column base and grout to take a portion of appled shear load, V, thus reducing the shear to be taken by bolts. The total shear to be taken by bolts, 'Vb(bolts)', is then calculated as follows: V(bolts) = V-1/2*m*P(DL) where: m = Coefficient of Friction = 0.55 for base plate on top of grout bed = 0.70 for base plate recessed in grout = 0.90 for base plate embedded in concrete P(DL) = portion of column load as dead load Note: in the value of column dead load, 'P(DL)', user may elect to also include ONLY the portion of column axial live load which produces shear, if any.

H404


I404


J404


K404

This is trial base plate thickness to be input by user, which will be compared to required thickness in results. Note: user may wish to compare input thickness to suggested minimum thickness to ensure rigidity, which is: tp(min) >= Maximum of: m/4 or n/4 where: m = (N-0.95*d)/2 n = (B-0.80*bf)/2 Note: suggested minimum base plate thickness for rigidity, is shown in Column AH.

L404

Pier length, 'Lpx', MUST BE >= base plate length, 'N'.

M404

Pier width, 'Lpy', MUST BE >= base plate width, 'B'.

N404

'Nb' is the total number of anchor bolts on both sides of the column flanges. Note: anchor bolts MUST be in only 2 rows, one row outside of each column flange. Note: MUST input whole number value of either 2, 4, 6, or 8.

O404

Anchor bolt diameters permitted are: 3/8", 1/2", 5/8", 3/4", 7/8", 1", 1-1/8", 1-1/4", 1-3/8", 1-1/2", 1-3/4", 2", 2-1/4", 2-1/2", 2-3/4", and 3".

P404


Q404


R404

The eccentricity (e) for Load Case 1 is: e = ABS(M*12/P)

S404


T404

The eccentricity (e) for Load Case 2 is: e = ABS(M*12/P)

U404


V404

Note: P = -P (which was input) for use in equations below. For case of axial compression load without moment: fp(max) = fp(min) = fp = P/(N*B) For case of axial compression load plus moment: when: ABS(e) = M*12/P > N/2-Xc/3 T = -P*(N/2-Xc/3-e)/(N/2-Xc/3+(N/2-ED1)) , Tb = T/(Nb/2) fp(max) = 2*(P+T)/(Xc*B) when: N/6 < ABS(e) <= N/2-Xc/3 fp(max) = 2*P/(Xc*B) when: ABS(e) <= N/6 fp(max) = ABS(P)/(N*B)*(1+6*e/N) For case of axial tension load plus moment: when: ABS(e) = M*12/P > N/2-ED1 Tb = -P*(N/2-ED1-M*12/P)/(2*(N/2-ED1))/(Nb/2) T = Tb*(Nb/2) fp(max) = 2*(P+T)/(Xc*B) when: ABS(e) <= N/2-ED1 fp(max) = 0

W404

Allowable concrete bearing stress, 'Fp', is determined as follows: for bearing on entire area of concrete support, Fp = 0.35*f'c for bearing on less than entire area of concrete support, Fp = 0.35*f'c*SQRT(A2/A1) <= 0.70*f'c where: A2 = Lpx*Lpy >= N*B A1 = N*B Note: the total bearing area of the concrete support, 'A2', MUST have a minimum value of A2 = N*B. For base plates supported on slabs or mats, use A2 = 4*(N*B).

Y404

Note: P = -P (which was input) for use in equations below. For column base plates subjected to concentric axial compression load without moment: fp = P/(N*B) , m = (N-0.95*d)/2 , n = (B-0.8*bf)/2 , n' = SQRT(d*bf)/4 q = 4*fp*d*bf/((d+bf)^2*Fp) < 1.0 , l = 2*(1-SQRT(1-q))/SQRT(q) <= 1.0 tp = 2*c*SQRT(fp/Fy) , where: c = maximum of: m, n, or l*n' For column base plates subjected to axial load plus moment: If Xc > m , tp = maximum of: tp = SQRT(6*((fpmax-((fpmax-fpmin)/Xc)*m)*m^2/2+((fpmax-fpmin)/Xc)*m^3/3)/(0.75*Fy)) tp = 2*n*SQRT((fpmax+fpmin)/2/Fy) tp = 2*(l*n')*SQRT((fpmax+fpmin)/2/Fy) tp = SQRT(6*Tb*(m-ED1)/be/(0.75*Fy)) If Xc <= m , tp = maximum of: tp = SQRT(6*fpmax*Xc/2*(m-Xc/3)/(0.75*Fy)) tp = SQRT(6*Tb*(m-ED1)/be/(0.75*Fy)) where: be = min. of: (m-ED1) or (B-2*ED2)/(2*(Nb/2-1)) + min. of: (m-ED1) or (B-2*ED2)/(2*(Nb/2-1)) or ED2

AA404

Note: P = -P (which was input) for use in equations below. For case of axial compression load plus moment: when: ABS(e) = M*12/P > N/2-Xc/3 , Tb > 0 T = -P*(N/2-Xc/3-e)/(N/2-Xc/3+(N/2-ED1)) Tb = T/(Nb/2) when: ABS(e) <= N/2-Xc/3 Tb = 0 For case of axial tension load plus moment: when: ABS(e) > N/2-ED1: Tb = -P*(N/2-Xc/3-M*12/P)/(N/2-Xc/3+(N/2-ED1))/(Nb/2) when: ABS(e) <= N/2-ED1: Tb = -P*(N/2-ED1-M*12/P)/(2*(N/2-ED1))/(Nb/2)

AB404

Anchor Bolt Data Nominal Diameter, db (in.) Area, Ab (in.^2) Allowable Tension, Ta (kips) A307 A36 A572 A588 F1554 (36) F1554 (55) F1554 (105) 1/2 0.1963 3.93 3.75 4.22 4.53 3.75 4.87 8.11 5/8 0.3068 6.14 5.86 6.60 7.09 5.86 7.61 12.67 3/4 0.4418 8.84 8.44 9.50 10.21 8.84 10.96 18.25 7/8 0.6013 12.03 11.48 12.93 13.89 11.48 14.91 24.83 1 0.7854 15.71 15.00 16.89 18.14 15.00 19.48 32.44 1-1/8 0.9940 19.88 18.98 21.37 22.96 18.98 24.65 41.05 1-1/4 1.2272 24.54 23.44 26.38 28.35 23.44 30.43 50.68 1-3/8 1.4850 29.70 28.36 31.93 34.30 28.36 36.83 61.33 1-1/2 1.7671 35.34 33.75 37.99 40.82 33.75 43.82 72.98 1-3/4 2.4053 48.11 45.94 51.71 55.56 45.94 59.65 99.34 2 3.1416 62.83 60.00 67.54 72.57 60.00 77.91 129.75 2-1/4 3.9761 79.50 75.94 85.49 91.85 75.94 98.61 164.21 2-1/2 4.9087 98.17 93.76 105.54 113.39 93.76 121.74 202.73 2-3/4 5.9396 118.79 113.45 127.70 137.20 113.45 147.30 245.31 3 7.0686 141.37 135.01 151.97 163.28 135.01 175.30 291.93 Note: allowable tension values are for no shear. Allowable Tension Stress and Min. Tensile Strength for Anchor Bolts Description of Anchor Bolts Ft (ksi) Fu (ksi) Fy (ksi) A307 bolts 20.0 60.0 36.0 A36 threaded rods 19.1 58.0 36.0 A572 threaded rods 21.5 65.0 50.0 A588 threaded rods 23.1 70.0 50.0 F1554 (Gr. 36) th'd. rods 19.1 58.0 36.0 F1554 (Gr. 55) th'd. rods 24.8 75.0 55.0 F1554 (Gr. 105) th'd. rods 41.3 125.0 105.0 Note: Ft = 0.33*Fu.

AD404

The actual bolt shear, 'Vb', is: Vb = V/Nb

AE404

Anchor Bolt Data Nominal Diameter, db (in.) Area, Ab (in.^2) Allowable Shear, Va (kips) A307 A36 A588 A572 F1554 (36) F1554 (55) F1554 (105) 1/2 0.1963 1.96 1.94 2.18 2.34 1.94 2.51 4.18 5/8 0.3068 3.07 3.04 3.41 3.65 3.04 3.93 6.53 3/4 0.4418 4.42 4.37 4.90 5.26 4.37 5.66 9.41 7/8 0.6013 6.01 5.95 6.67 7.16 5.95 7.70 12.81 1 0.7854 7.85 7.78 8.72 9.35 7.78 10.05 16.73 1-1/8 0.9940 9.94 9.84 11.03 11.83 9.84 12.72 21.17 1-1/4 1.2272 12.27 12.15 13.62 14.60 12.15 15.71 26.14 1-3/8 1.4850 14.85 14.70 16.48 17.67 14.70 19.01 31.63 1-1/2 1.7671 17.67 17.49 19.62 21.03 17.49 22.62 37.64 1-3/4 2.4053 24.05 23.81 26.70 28.62 23.81 30.79 51.23 2 3.1416 31.42 31.10 34.87 37.38 31.10 40.21 66.92 2-1/4 3.9761 39.76 39.36 44.13 47.32 39.36 50.89 84.69 2-1/2 4.9087 49.09 48.60 54.49 58.41 48.60 62.83 104.56 2-3/4 5.9396 59.40 58.80 65.93 70.68 58.80 76.03 126.51 3 7.0686 70.69 69.98 78.46 84.12 69.98 90.48 150.56 Note: allowable shear values are for no tension. Allowable Shear Stress on Anchor Bolts Description of Anchor Bolts Fv (ksi) A307 bolts 10.0 A36 threaded rods 9.9 A572 threaded rods 11.1 A588 threaded rods 11.9 F1554 (Gr. 36) th'd. rods 9.9 F1554 (Gr. 55) th'd. rods 12.8 F1554 (Gr. 105) th'd. rods 21.3 Note: Fv = 0.17*Fu (for threads included in shear plane).

AG404

Stress ratio for interaction of combined anchor bolt tension and shear is calculated as follows: S.R. = Tb/Ta+(C*Vb)/Va <= 1.0 where: C = Shear Coefficient = 1.85 for base plate on top of grout bed = 1.25 for base plate recessed in grout = 1.10 for base plate embedded in concrete References: 1. "Design Aid: Anchor Bolt Interaction of Shear and Tension Loads" by Mario N. Scacco AISC Engineering Journal, 4th Quarter - 1992. 2. "Design of Headed Anchor Bolts" by John G. Shipp and Edward R. Haninger AISC Engineering Journal, 2nd Quarter - 1983.

steel base plate design

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