"CIRCBASE" --- STEEL COLUMN CIRCULAR BASE PLATE ANALYSIS Program Description: "CIRCBASE" is a spreadsheet program written in MS-Excel for the purpose of analysis of steel column base plates. Specifically, pipe columns base plates may be subjected subjected to axial loads (compression only), with or without column bending, bending, plus shear. Base plate bearing pressure is checked as well as bolt tension, if applicable. If shear is present, bolt shear as well well as interaction of bolt tension and and shear, if applicable, are calculated. Finally, a propoesed propoesed base plate thickness is is checked. checked.
This program is a workbook consisting of two (2) worksheets, described as follows:
Worksheet Name
Description
Doc Complete method
This documentation sheet Circular base plate analysis
Program Assumptions and Limitations: 1. This program follows the the procedures and and guidelines of "Design "Design of Monopole Monopole Bases", by Daniel Horn, P.E. 2. This program follows the procedures procedures and guidelines of the AISC 9th 9th Edition Allowable Stress Stress (ASD) Manual (2nd Revision, 1995) for round hollow structural tube & column base plates subjected to flexure. 3. For steel interaction interaction of anchor bolt tension and shear, shear, this program follows: Appendix D of of ACI 318-02, "Building Code Requirements For Structural Structural Concrete" 4. For concrete bearing, this program follows: Section 10.17 of ACI 318-02, "Building Code Requirements For Structural Concrete" 5. User has option to take out some some of the total shear though though friction between column column base and grout based based on column dead load and coefficient of friction, thus reducing amount of shear to be taken by anchor bolts. 6. Additional assumptions assumptions used used in this program are as follows: a. T he column is centered on a circular base plate in both directions. b. The column & base plate are centered on a round pedestal in both directions. b. Axial column load, 'P' > 0 for the case with moment.
7. This program contains numerous “comment “comment boxes” which contain a wide variety of information including explanations of inpu inputt or output items, equations used, data tables, etc. (Note: presence of a “comment box” is denoted denoted by a “red triangle” in the upper upper right-hand right-hand corner corner of a cell. Merely move the the mouse mouse pointer pointer to the desired cell to view the contents of that particular "comment box".) 8. For the addition of gusset plates to the baseplate, this program derives the baseplate moments moments from "Theory of Plates and Shells", by S. Tomonshenko. (1st Edition, 1940) a. Table 26 - Deflection & Bending Moments for a Uniformly Loaded Plate with Two Opposite Edges Simply Supported, the Third Edge Free and the Fourth is Built In (Page 218)
GROUTED BASE PLATES Per AISC 9th Edition Manual (ASD) and "Design of Monopole Bases" (Daniel Horn, P.E.) based on the Complete Circular Base Plate Method Job Name: Job No.: Subject: Originator: Checker: Input Data: Column Loadings: Axial Load, P = Axial Load, P(DL) = Shear Load, V = Moment @ Base, M =
11.00 0.00 3.00 974.00
Design Parameters: Mod./High seismic risk region? Is a grout pad present? Column Outer Dia., OD (col) = Column wall thick, t col = Column Yield stress, F y(col) = Base Plate O.D., B = Base Plate I.D., di = Base Plate thick, t (PL) = Plate Yield Stress, Fy = Baseplate gussets present? Gusset Plate thick, t g = Gusset Plate height, h g = No. of Gusset Plates, N g = Concrete Strength, f 'c = Coef. of Friction, μ = Conc. Ped. diameter, OD (ped) = ACI load factor, LF =
Yes Yes 16.000 0.500 35.000 25.000 16.000 1.750 36.00 Yes 0.500 12.000 8 4.000 0.55 30.00 1.38
Anchor Bolt/Rod Data: Total No. of Bolts, Nb = Bolt Circle Dia, BC = Bolt Diameter, db = Anchor Bolt Material =
6 20.00 1 1/4 F1554 (36)
kips kips kips in-kips
PL bearing area
e = 88.55 in y = 9.95 in
yo = 2.55 in
in in ksi in in in ksi
di = 16 in
in in BC = 20 in
ksi
B = 25 in
in
bolts in in
Iteration: q(start) = q(calc) = Delta =
86.0000 83.4276 2.5724
in in
Start value should approx. equal eccentricity Change q(start) until Delta = 0.
Results: Calculate the area of the outer circle: r= y = lo = yo = A1 =
12.50 9.95 2.55 182.24
in = B/2 in = r-e+q in = r-lo in^2 = r^2* p/2-yo*√(r^2-yo^2)-r^2*asin(yo/r)
(continued)
Complete Method
GROUTED BASE PLATES Per AISC 9th Edition Manual (ASD) and "Design of Monopole Bases" (Daniel Horn, P.E.) based on the Complete Circular Base Plate Method Job Name: Job No.: Subject: Originator: Checker: Results (continued): Calculate the area of the inner circle ri = l = yc = Ac = AT = y1 = Q1 = y1c = Qc = QT =
8.00 5.45 2.55 -60.50 166.55 6.70 14,915 4.81 -5,066 13,833
in = di/2 in = ri-e+q in = max(ri- l or -ri), or 0 if l<0 in^2 = -ri^2* p/2+yc*√(ri^2-yc^2)+ri^2*asin(yc/ri), or 0 if l<0
in^2 = A1+Ac+Σ(n-1)*Ab+Σn*Ab in = [2*(r^2-yo^2)^1.5]/3*A1 in^3 = A1*(e-y1) in = 0 if l<0, or [-2*(ri^2-yc^2)^1.5]/(3*Ac) in^3 =Ac*(e-y 1c), or 0 if l<0 in^3 = Q1 + Q bolt + Qc
Calculate the moments of inertia I1 = Ic = Ibolt = IT = q(calc) =
1,221,916 -424,371 356,488 1,154,032 83.43
in^4 in^4 in^4 in^4 = I1+Ic+Ibolt in = IT/QT
Concrete Results: Eccentricity, e = Min. Eccentricity, e(min) =
ACI load factor, LF = Conc bearing stress, f c(max) = Factored bear stress, f c(max,f) = ybc = Conc bearing stress, f bc = Factored bearing stress, f bc,f =
Strength reduction factor, Φ = PL to ped edge dist, d1a = Min. bear length, d1 = Conc bear area O.D., OD (bear) = Conc bear area I.D., ID (bear) = Baseplate bearing area, A PL = Concrete bearing area, A conc = √(Aconc/APL) = Allow. bear. stress, f c(allow) =
88.55 in = ABS(M/P) 4.41 in = (B^4-di^4)/(8*B*(B^2-di^2)) Method Valid 1.38 1.77 2.44 4.88 0.87 1.53 0.65 2.50 2.50 30.00 11.00 289.81 611.83 1.45 3.21
ksi = P*y/(q*A T-QT) ksi = LF*f c(max) in = BC/2-e+q (calc) ksi @ bolt circle = P*y bc/(q*AT-QT) ksi @ bolt circle = LF*f bc in = [OD(ped)-di]/2 in = min[ d1a , r(col) ] in = B+2*d1 in = di-2*d1 in^2 = p/4*(B^2-di^2) in^2 = p/4*[OD (bear)^2-ID(bear)^2]
ksi = Φ*0.85*(f 'c)*√(Aconc/APL) fc(max,f) ≤ fc(allow), O.K.
Steel Results: beff = y= f pole =
8.38 2.88 0.51
in = p*B/Nb in = B/2-e+q (calc) ksi = P*y/[q (calc)*AT-QT]
(continued)
Steel Results (continued): Complete Method
GROUTED BASE PLATES Per AISC 9th Edition Manual (ASD) and "Design of Monopole Bases" (Daniel Horn, P.E.) based on the Complete Circular Base Plate Method Job Name: Job No.: Subject: Originator: Checker: Compression Side: No. of Gusset Plates, N g = Gusset spacing, b = Baseplate Length, L = L/b = L/b
8.00 10.73 4.50 0.42
plates in = 2*p*([r+r (col)]/2)/Ng in = 0.5[B-OD (col)]
Mx x = b/2
My y = L1
x = b/2
y=0
0
0
-0.500 fc*L^2
0.333
0.0078 fc*b^2
-0.428 fc*L^2
0.5
0.0293 fc*b^2
-0.319 fc*L^2
0.667
0.0558 fc*b^2
-0.227 fc*L^2
1
0.0972 fc*b^2
-0.119 fc*L^2
1.5
0.1230 fc*b^2
-0.124 fc*b^2
2
0.1310 fc*b^2
-0.125 fc*b^2
3
0.1330 fc*b^2
-0.125 fc*b^2
∞
0.1330 fc*b^2
-0.125 fc*b^2
Conc bearing stress, f c(max) = Cx = Mx = Cy = My = M(max) = f (max) = f (all) =
1.77 0.0189 3.845 -0.3718 -13.310 13.31 4.99 27.00
This table is taken from Theory Of Plates And Shells (Timoshenko)
ksi = P*y/(q*A T-QT) in-kips/in = Cx*fc*b^2 in-kips/in = Cy*fc*L^2 in-kips ksi = [6*M(max)]/t(PL)^2 ksi = 0.75*F y
f(max) ≤ f(all), O.K.
f(max) ≤ f(all), O.K.
Tension Side: M(max) = f (max) = f (all) =
38.12 8.92 27.00
in-kips = Pten*[BC-OD(col)]/2 ksi = 6*M*(max)/[beff*t(PL)^2] ksi = 0.75*Fy
Gusset spacing, b = Rcol = m= a= Z= Vg = Mg = f b(pole wall) = f b(allow) =
10.73 8.00 1.75 2.00 0.21 85.38 192.11 13.78 21.00
in = 2*p*([r+r(col)]/2)/Ng in = OD(col)/2 in = t(PL) in = 2*(tg+t) = 1/[ (0.177*a*m/sqrt(R col*t))(m/tcol)^2+1.0] kips = fc*b*L in-kips = ½*fc*b*L^2 ksi ksi = 0.6*Fy(col) fb(pole wall) ≤ fb(allow), O.K.
201.06 4.84 14.85 0.326
in^2 =(p/4)*OD (col)^2 kips/in = M/S weld ksi = 0.7071*0.3*(70 ksi) in = f wm/σw
Column Wall:
Column to Baseplate Weld: Sweld = Weld force, f wm = Allowable weld stress, σ w = Req'd weld size, ω h =
Weld design assumes 70 ksi electrodes
(continued)
Steel Results (continued):
Complete Method
GROUTED BASE PLATES Per AISC 9th Edition Manual (ASD) and "Design of Monopole Bases" (Daniel Horn, P.E.) based on the Complete Circular Base Plate Method Job Name: Job No.: Subject: Originator: Checker: Gusset / Column / Baseplate Weld:
tg = 0.5 in hg = 12 in Weld design assumes 70 ksi electrodes
t(PL) = 1.75 in b1 = 6.28 in
Determine moment of inertia of gusset/baseplate section Item 1 2
b 6.28 0.50 Totals
h 1.75 12.00 13.75
y 0.88 7.75
Baseplate effective width, b 1 = Location of gusset/basepl neutral axis, y bar = Gusset/basepl moment of inertia, I1 = # of welds, N w = Allowable weld stress, σ w = Bending stress @ t.o. gusset, σ t = Bending stress @ b.o. gusset, σ b = Shear force @ face of baseplate, f v = Horizontal weld force, f vw = Horizontal req'd weld size, ω h = Bending force on vert. weld, f bw = Vertical shear on weld, f sw = Resultant weld force, f rw = Req'd weld size, ω v =
A 11.00 6.00 17.00
6.28 3.30 258.28 2.00 14.85 7.77 2.46 8.82 4.41 0.30 1.94 3.56 4.05 0.27
A*y 9.62 46.50 56.12
A*y^2 8.42 360.38 368.79
Io
2.81 72.00 74.81
in = p*OD(col)/Ng
in = ΣA*y/ΣA in^4 = ΣIo+Σ(A*y^2)-Σ[(A*y)*y bar ] welds ksi = 0.7071*0.3*(70 ksi) ksi ksi kips/in = V g*[(b1)*t(PL)]*[ybar -½*t(PL)]/I1 kips/in = f v/Nw in = f vw/σw
k/in = σt*tg/Nw k/in = Vg/(hg*Nw) k/in = SQRT(f bw^2+f sw^2) in = f rw/σw
(continued)
Anchor Bolt/Rod Steel Tension and Shear (Per ACI 318-02):
Tensile strength reduction factor, Φ =
0.75 Complete Method
GROUTED BASE PLATES Per AISC 9th Edition Manual (ASD) and "Design of Monopole Bases" (Daniel Horn, P.E.) based on the Complete Circular Base Plate Method Job Name: Job No.: Subject: Originator: Checker: Shear strength reduction factor, Φ = 0.65 ACI load factor, LF = 1.38 in = p*BC/Nb A.B. Spacing, s = 10.47 Max. bolt tension, P ten = Tb = N = 19.06 kips (See following page) Max. factored bolt tension, N u = 26.30 kips = LF*N Bolt Shear, V (bolts) = kips = V(total)-1/2*μ *P(DL) 3.00 Bolt Shear, V b = Vu = kips/bolt = V (bolts)/Nb 0.69 Ase = 0.97 in^2 Fy(bolt) = 36.00 ksi Fut(bolt) = 58.00 ksi ΦNs = 31.61 kips/bolt = 0.75*Φ*Ase*Fut(bolt) ΦVs = 13.15 kips/bolt = 0.75*0.8*Φ*0.6*Ase*Fut(bolt) = Nu/(ΦNs) Tension interaction = 0.832 S.R. ≤ 1.00, O.K.! = Vu/(ΦVs) Shear interaction = 0.042 S.R. ≤ 1.00, O.K.! = Nu/(ΦNs) + Vu/(ΦVs) Interaction check = 0.885 S.R. ≤ 1.20, O.K.! Steel anchor strength is OKAY! * Shear strength of anchors with grout pads shall be multiplied by 0.8 ACI 318-02, Sect. D.6.1.3 * Anchor strength reduced by 75% due to seismic region ACI 318-02, Sect. D3.3.3
(continued)
Individual Anchor Bolt Forces: Bolt # 1
ybolt 0.00
n 8.04
Abt 0.969
n*Abolt 7.79
Qbolt 689.84
Ibolt
61086.71
Pbolt 7.08 Complete Method
GROUTED BASE PLATES Per AISC 9th Edition Manual (ASD) and "Design of Monopole Bases" (Daniel Horn, P.E.) based on the Complete Circular Base Plate Method Job Name: Job No.: Subject: Originator: Checker: 2 8.66 7.04 0.969 6.82 544.96 43537.76 -4.29 3 8.66 7.04 0.969 6.82 544.96 43537.76 -4.29 4 0.00 8.04 0.969 7.79 689.84 61086.71 7.08 5 -8.66 8.04 0.969 7.79 757.31 73619.33 19.06 6 -8.66 8.04 0.969 7.79 757.31 73619.33 19.06
Totals Max bolt tension, N =
19.06
44.81
3984
356,488
kips
Note: 1. Tension (uplift) load = positive (+) 2. Compression (downward) load = negative (-) 3. Qbolt = Σ n*Abolt*(e-ybolt) 4. n*Abolt = n*Abt (tension zone) 5. n*Abolt = (n-1)*A bt (compression zone) 6. Ibolt = Σ[ n*A bt^2/(4p) + n*A bt*(e-ybolt)^2] 7. Pbolt = P*[e-y bolt-q(calc)]/(q(calc) *AT-QT)*[n*A bt] Comments: 1. Controlling strength design load case was 1.2*[Ds+Do+AF]+1.0*E(+Z) where Mx = 1340 in-kips. 2. Controlling service load case was Ds+Do+AF+0.7*E(+Z) where Mx = 974 in-kips. 3. ACI concrete load factor used for design = (1340 in-k)/(974 in-k) = 1.376, say 1.38.
Complete Method
