Footings - Rectangular Spread Footing Analysis
Footings - Rectangular Spread Footing Analysis
Footings - Rectangular Spread Footing Analysis
Program Description:
"FOOTINGS" is a spreadsheet program written in MS-Excel for the purpose of analysis of rigid rectangular spread footings with up to 8 total piers, and for either uniaxial or biaxial resultant eccentricities. Overturning sliding, and uplift stability checks are made when applicable, and resulting gross soil bearing pressures at the four (4) corners of the footing are calculated. The maximum net soil bearing pressure is also determined. This program is a workbook consisting of five (5) worksheets, described as follows:
Worksheet Name
Doc Footing (net pier loads) Footing (breakdown of loads) Footings (Table) Footings (Pier Table)
Description
This documentation sheet Individual rectangular spread footing analysis (with net pier loadings) Individual rectangular spread footing analysis (with breakdown of loadings) Multiple rectangular spread footings analysis and design (table format) Multiple rectangular spread footings - pier analysis (table format)
This worksheet should be specifically used in any of the following conditions: a. When the individual breakdown of loadings is known or is critical b. When there are uplift or overturning forces and moments due to wind (or seismic) c. When the factor of safety against uplift or overturning due to wind (or seismic) is critical d. When there are no overturning forces or moments due to only gravity (dead or live) loadings 10. The "Footing (breakdown of loads)" worksheet considers only applied wind (or seismic) shears, uplifts, and moments as forces causing overturning. Any wind (or seismic) loads which act in opposite direction to sense of overturning are considered as forces which reduce the total overturning. Only applied pier dead (not live) loadings are considered as forces resisting overturning. Any dead loadings which act in opposite direction to sense of resisting overturning are considered as forces which reduce the total resistance to overturning. 11. This program includes the uniform live load surcharge in the calculation of the soil bearing pressures. The uniform live load surcharge is not included in the calculation of "resisting" moment for overturning check, nor in the calculations for uplift check. The uniform live load surcharge is assumed to act over the entire footing plan area. 12. This program will calculate the soil bearing pressures at the corners of the footing for all cases of resultant eccentricity, both uniaxial and biaxial. The corners of the footing are always designated in the footing plan proceeding counterclockwise from the lower right-hand corner as follows: (3) = upper left-hand corner (2) = upper right-hand corner (4) = lower left-hand corner (1) = lower right-hand corner 13. Reference used in this program for footing with cases of biaxial resultant eccentricity is: "Analytical Approach to Biaxial Eccentricity" - by Eli Czerniak Journal of the Structural Division, Proceedings of the ASCE, ST4 (1962), ST3 (1963) 14. Another more recent reference for footing with cases of biaxial resultant eccentricity is: "Bearing Pressures for Rectangular Footings with Biaxial Uplift" - by Kenneth E. Wilson Journal of Bridge Engineering - Feb. 1997 15. The "Footings (Table)" and "Footings (Pier Table)" worksheets enable the user to analyze/design virtually any number of individual footings or footing load combinations. The footings must have only one concentric pier. The footings may be subjected to biaxial eccentricities as long as 100% bearing is maintained. If one or more corners become unloaded from biaxial eccentricities, then the error message, " Resize! " will be displayed. Refer to those two worksheets for list of specific assumptions used in each. The column loads and footing/pier dimensions input in rows "A" through "Q" of the "Footings (Table)" worksheet may be copied and pasted (via "Paste Special, Values " command) into the same position in the "Footings (Pier Table)" worksheet. The entire row of calculation cells can then be copied and pasted down the page to match the number of rows of input in each of the two table format worksheets. 16. 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".)
For Assumed Rigid Footing with from 1 To 8 Piers Subjected to Uniaxial or Biaxial Eccentricity Subject: Originator:
+Pz +My
Checker:
Footing Length, L = Footing Width, B = Footing Thickness, T = Concrete Unit Wt., gc = Soil Depth, D = Soil Unit Wt., gs = Pass. Press. Coef., Kp = Coef. of Base Friction, m = Uniform Surcharge, Q = Pier/Loading Data: Number of Piers = Pier #1 0.000 0.000 2.000 2.000 3.000 -80.00 20.00 0.00 0.00 0.00
Lpx
ksf
Nomenclature
Xp (ft.) = Yp (ft.) = Lpx (ft.) = Lpy (ft.) = h (ft.) = Pz (k) = Hx (k) = Hy (k) = Mx (ft-k) = My (ft-k) =
FOOTING PLAN
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Results: Total Resultant Load and Eccentricities: SPz = -110.44 kips ex = 0.906 ft. (<= L/6) ey = 0.000 Overturning Check: SMrx = N.A. SMox = N.A. FS(ot)x = N.A. SMry = 409.76 SMoy = 100.00 FS(ot)y = 4.098 Sliding Check: Pass(x) = Frict(x) = FS(slid)x = Passive(y) = Frict(y) = FS(slid)y = Uplift Check: SPz(down) = SPz(uplift) = FS(uplift) =
Nomenclature for Biaxial Eccentricity: Case 1: For 3 Corners in Bearing (Dist. x > L and Dist. y > B)
Dist. x Pmax
Brg. Ly
Dist. y
Brg. Lx
Case 2: For 2 Corners in Bearing (Dist. x > L and Dist. y <= B) 10.80 40.98 2.589 17.28 40.98 N.A.
kips kips (>= 1.5) kips kips
Dist. x Pmax
Brg. Ly1
Dist. y Brg. Ly2
kips kips
Bearing Length and % Bearing Area: Dist. x = N.A. ft. Dist. y = N.A. ft. Brg. Lx = 8.000 ft. Brg. Ly = 5.000 ft. %Brg. Area = 100.00 % Biaxial Case = N.A. Gross Soil Bearing Corner Pressures: P1 = 4.636 ksf P2 = 4.636 ksf P3 = 0.886 ksf P4 = 0.886 ksf
Dist. y
Brg. Lx1
P2=4.636 ksf
P1=4.636 ksf
CORNER PRESSURES
Dist. y Brg. Ly
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For Assumed Rigid Footing with from 1 To 8 Piers Subjected to Uniaxial or Biaxial Eccentricity Subject: Originator:
+Pz +My
Checker:
Footing Length, L = Footing Width, B = Footing Thickness, T = Concrete Unit Wt., gc = Soil Depth, D = Soil Unit Wt., gs = Pass. Press. Coef., Kp = Coef. of Base Friction, m = Uniform Surcharge, Q = Pier/Loading Data: Number of Piers = Pier #1 -3.000 0.000 2.500 2.000 3.000 -5.00 -5.00 40.00 0.00 0.00 20.00 0.00 0.00 10.00 0.00 0.00 -10.00 0.00 0.00 10.00
Q
Lpx
ksf
2 Pier #2 3.000 0.000 2.500 2.000 3.000 -30.00 -10.00 -40.00 0.00 0.00 10.00 0.00 0.00 0.00 0.00 0.00 -10.00 0.00 0.00 20.00
Y
Nomenclature
Xp (ft.) = Yp (ft.) = Lpx (ft.) = Lpy (ft.) = h (ft.) = Pz(D) (k) = Pz(L) (k) = Pz(W) (k) = Hx(D) (k) = Hx(L) (k) = Hx(W) (k) = Hy(D) (k) = Hy(L) (k) = Hy(W) (k) = Mx(D) (ft-k) = Mx(L) (ft-k) = Mx(W) (ft-k) = My(D) (ft-k) = My(L) (ft-k) = My(W) (ft-k) =
FOOTING PLAN
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Results: Total Resultant Load and Eccentricities: S Pz = -194.50 kips ex = 2.776 ft. (> L/6) ey = 0.411 ft. (<= B/6) Overturning Check: SMrx = 737.50 SMox = -80.00 FS(ot)x = 9.219 SMry = 1105.00 SMoy = 450.00 FS(ot)y = 2.456 Sliding Check: SHx(D)Resist = Pass(x) = Frict(x) = FS(slid)x = SHy(D)Resist = Pass(y) = Frict(y) = FS(slid)y = Uplift Check: SPz(down) = SPz(uplift) = FS(uplift) = Nomenclature for Biaxial Eccentricity: Case 1: For 3 Corners in Bearing (Dist. x > L and Dist. y > B)
Dist. x Pmax
ft-kips ft-kips (>= 1.5) ft-kips ft-kips (>= 1.5)
Brg. Ly
Dist. y
Brg. Lx
kips kips kips (>= 1.5) kips kips kips (>= 1.5)
Bearing Length and % Bearing Area: Dist. x = 17.497 ft. Dist. y = 44.895 ft. Brg. Lx = 13.600 ft. Brg. Ly = 3.842 ft. %Brg. Area = 95.38 % Biaxial Case = Case 1 6*ex/L + 6*ey/B = 1.288 Gross Soil Bearing Corner Pressures: P1 = 2.179 ksf P2 = 2.804 ksf P3 = 0.240 ksf P4 = 0.000 ksf
Dist. y
Line of zero pressure Brg. Lx1
P2=2.804 ksf
P1=2.179 ksf
CORNER PRESSURES
Dist. y Brg. Ly
Line of zero pressure
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Input Data: +Y Allow. Net Soil Pressure, Pa(net) = Soil Unit Weight, gs = Passive Pressure Coefficient, Kp = Coefficient of Base Friction, m = Concrete Unit Weight, gc = Conc. Compressive Strength, f'c = Reinforcing Yield Strength, fy = USD Load Fact. for Concrete, LF = Design for P(max)net or Pa(net) ? 3.000 0.120 3.000 0.400 0.150 3 60 1.6 P(max)
ksf kcf
+My
3 L/2
2
Q
+Hx
Lpx
kcf ksi ksi
Lpy
Lpx
+X
B/2
B T
L Footing Plan
Footing Elevation
Assumptions: 1. For uniaxial eccentricity (either ex or ey) the maximum gross soil pressure is calculated as follows: for ex <= L/6: P(max)gross = ( S Pz)/(B*L)*(1+6*ABS(ex)/L) and P(min)gross = ( S Pz)/(B*L)*(1-6*ABS(ex)/L) , for ex > L/6: P(max)gross = (2* S Pz)/(3*B*(L/2-ABS(ex))) and P(min)gross = 0 for ey <= B/6: P(max)gross = ( S Pz)/(L*B)*(1+6*ABS(ey)/B) and P(min)gross = ( S Pz)/(L*B)*(1-6*ABS(ey)/B) , for ey > B/6: P(max)gross = (2* S Pz)/(3*L*(B/2-ABS(ey))) and P(min)gross = 0 where: S Pz = summation of vertical load and all weights = applied column vertical load (Pz) + soil weight + excess pier weight + surcharge (Q). 2. Concurrent biaxial eccentricities (both ex and ey) are permitted up to point where full contact (100% bearing) on the footing base is still maintained. P(max)gross = ( S Pz)/(B*L)*(1+6*ABS(ex)/L+6*ABS(ey)/B) and P(min)gross = ( S Pz)/(B*L)*(1-6*ABS(ex)/L-6*ABS(ey)/B) where: controlling biaxial eccentricity criteria is as follows: 6*ABS(ex)/L+6*ABS(ey)/B <= 1.0 3. Maximum net soil pressure is calculated as follows: P(max)net = P(max)gross-(D+T)* gs >= 0 4. Program considers all applied moments and horizontal loads as forces causing overturning. However, uplift load (Pz > 0) is considered as a force causing overturning only when there is an applicable resultant eccentricity in the direction of overturning. Combination of frictional resistance between footing base and soil as well as passive soil pressure against footing base and pier is used for total sliding resistance. 5. Program includes uniform live load surcharge (Q) in calculation of soil bearing pressures, and is assumed to act over entire footing plan area (L*B). Uniform live load surcharge (Q) is not included in any of stability checks. 6. One-way and two-way shear capacity checks are based on full uniform design net bearing pressure, P(net) = either P(max)net or Pa(net), as selected by user. 7. Footing flexural reinforcing for bottom face is based on full uniform design net bearing pressure, P(net) = either P(max)net or Pa(net), as selected by user. Footing flexural reinforcing for top face is determined only when there is an applied column uplift load (Pz > 0), and is based on bending from footing self-weight plus any soil and live load surcharge (Q) weight. 8. Minimum temperature reinforcing is determined as follows: As(temp) = r(temp)*12*T (all reinforcing placed in bottom face only) for no column uplift and with soil cover (D > 0) As(temp) = r(temp)/2*12*T (reinforcing divided equally between top/bottom faces) for either with column uplift and/or no soil cover (D = 0) where: r(temp) = 0.0020 for fy = 40 or 50 ksi, r(temp) = 0.0018 for fy = 60 ksi, and r(temp) = 0.0018*60/fy for fy > 60 ksi. 9. For rectangular footings, the flexural reinforcing (per foot) running in the short direction is calculated by: As(short) = r(short)*12*d*2*b /(b +1) , where b = ratio of LongSide to ShortSide. SOIL DATA & SURCHARGE Depth Surch. D Q
(ft.) (ksf)
U in
COLUMN LOCATION
Axial Pz
(kips)
COLUMN LOADS Case 1: Maximum Load Condition Shear Shear Moment Moment Axial Hx Hy Mx My Pz
(kips) (kips) (ft-kips) (ft-kips) (kips)
Moment My
(ft-kips)
FOOTING DATA Pier Dimensions Base Dimensions Length Width Height Length Width Thickness Lpx Lpy h L B T
(ft.) (ft.) (ft.) (ft.) (ft.) (ft.)
Stability Checks F.S. F.S. F.S. F.S. Overturning Overturning Sliding Sliding
X-axis Y-axis X-direction Y-direction
RESULTS Shear Capacity Checks One-Way One-Way Two-Way Vu/fVc Vu/fVc Vu/fVc
X-direction Y-direction
Footing Reinforcing Bottom Face Top Face X-direction Y-direction X-direction Y-direction
(in.^2/ft.) (No. - Size) (in.^2/ft.) (No. - Size) (in.^2/ft.) (No. - Size) (in.^2/ft.) (No. - Size)
Footing
A-1 A-2 A-3 A-4 A-5 A-6 A-7 A-8 A-9 A-10 A-11 A-12
3.000 3.000 2.000 2.000 3.000 3.000 2.000 2.000 3.000 3.000 2.000 2.000
2.000 2.000 3.000 3.000 2.000 2.000 3.000 3.000 2.000 2.000 3.000 3.000
3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000
12.000 12.000 8.000 8.000 12.000 12.000 8.000 8.000 12.000 12.000 8.000 8.000
8.000 8.000 12.000 12.000 8.000 8.000 12.000 12.000 8.000 8.000 12.000 12.000
2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000
2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000
0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200
3.305 3.305 3.305 3.305 3.305 3.305 3.305 3.305 1.430 1.430 1.430 1.430
2.825 2.825 2.825 2.825 2.825 2.825 2.825 2.825 0.950 0.950 0.950 0.950
0.57 0.57 0.30 0.30 0.57 0.57 0.30 0.30 0.19 0.19 0.10 0.10
0.30 0.30 0.57 0.57 0.30 0.30 0.57 0.57 0.10 0.10 0.19 0.19
0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.17 0.17 0.17 0.17
0.522 0.522 0.518 0.518 0.522 0.522 0.518 0.518 0.518 0.518 0.518 0.518
9 - #7 9 - #7 13 - #7 13 - #7 9 - #7 9 - #7 13 - #7 13 - #7 9 - #7 9 - #7 13 - #7 13 - #7
0.518 0.518 0.522 0.522 0.518 0.518 0.522 0.522 0.518 0.518 0.518 0.518
13 - #7 13 - #7 9 - #7 9 - #7 13 - #7 13 - #7 9 - #7 9 - #7 13 - #7 13 - #7 9 - #7 9 - #7
-------------------------
-------------------------
-------------------------
-------------------------
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Assumptions: 1. 2. 3. 4. Y
d' (typ.)
Input Data: +Y Concrete Unit Weight, gc = Conc. Compressive Strength, f'c = Reinforcing Yield Strength, fy = USD Load Fact. for Concrete, LF = Clear Cover to Pier Ties, dc = 0.150 3 60 1.6 2.000
kcf ksi ksi in.
+My +Hx Q
5.
L/2
D h
Lpy
+X
Lpx B/2
S
B Ldh T
Lpy
Nsb (total)
Ntb (total)
6. 7. 8.
Footing Elevation
Pier Section
9.
Program uses CRSI's "Universal Column Formulas" in developing uniaxial interaction curves for X and Y axes, each load case. CRSI's "Universal Column Formulas" assume use of fy = 60 ksi. Program assumes "short", non-slender column analysis for pier. For cases with axial load only (compression or tension) and no moments (Mx and My = 0) the program calculates total reinforcing area (Ast) as follows: Ast = (Ntb + Nsb)*Ab , where: Ab = area of one bar For pure moment capacity with no axial load, program assumes bars in 2 outside faces parallel to axis of bending plus 50% of the total side bars divided equally by and added to the 2 outside faces, and calculated reinforcing areas as follows: for X-axis: As = A's = ((Ntb + 0.50*Nsb)*Ab)/2 , where: Ab = area of one bar for Y-axis: As = A's = (((Nsb+4) + 0.50*(Ntb-4))*Ab)/2 Reinforcing ratio shown is as follows: rg = (Ntb + Nsb)*Ab/(Lpx*12*Lpy*12). Axial load and flexural uniaxial design capacities, fPn and fMn, at design eccentricity, e = Mu*12/Pu, are determined from interpolation within the interaction curve for each axis. Axial load and flexural biaxial capacities, if applicable, are determined by the following approximations: a. For Pu >= 0.1*f'c*Ag, use Bresler Reciprocal Load Equation: 1/fPn = 1/fPnx + 1/fPny - 1/fPo Biaxial interaction stress ratio, S.R. = Pu/fPn <= 1 b. For Pu < 0.1*f'c*Ag, use Bresler Load Contour interaction equation: Biaxial interaction stress ratio, S.R. = (Mux/fMnx)^1.15 + (Muy/fMny)^1.15 <= 1 Straight-line interaction formula is used for biaxial shear interaction stress ratio, S.R. = Vux/ fVnx + Vuy/fVny <= 1 RESULTS Case 2: Axial and Flexural Capacity Checks X-axis Y-axis Biaxial Pu/fPnx Mux/fMnx Pu/fPny Muy/fMny S.R. 0.02 0.02 0.25 0.25 --------0.02 0.02 0.25 0.25 ----0.25 0.25 ------------0.25 0.25 0.25 0.25 0.02 0.02 --------0.25 0.25 0.02 0.02 0.25 0.25 ------------0.25 0.25 -----------------------------
Axial Pz
(kips)
Moment My
(ft-kips)
FOOTING DATA PIER REINFORCING DATA Pier Dimensions Base Dimensions Top/Bot. Side Vert. Horiz. Tie Horiz. Tie Reinf. Length Width Height Length Width Thickness Vert. Bars Vert. Bars Bar Size Bar Size Bar Spac. Ratio rg=Ast/Ag Lpx Lpy h L B T Ntb Nsb (#3 - #11) (#3 - #6) S
(ft.) (ft.) (ft.) (ft.) (ft.) (ft.) (in.)
Case 1: Axial and Flexural Capacity Checks X-axis Y-axis Biaxial Pu/fPnx Mux/fMnx Pu/fPny Muy/fMny S.R. 0.22 0.22 0.23 0.23 0.22 0.22 0.23 0.23 ------------0.23 0.23 ----0.23 0.23 --------0.23 0.23 0.22 0.22 0.23 0.23 0.22 0.22 --------0.23 0.23 ----0.23 0.23 -------------------------------------
X-direction Y-direction
Max. Shear Checks Biaxial Vu/fVnx Vu/fVny S.R. 0.12 0.12 ----0.11 0.11 ----0.12 0.12 --------0.12 0.12 ----0.11 0.11 ----0.12 0.12 -------------------------
Bearing Check Pu/fPnb 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.01 0.01 0.01 0.01
A-1 A-2 A-3 A-4 A-5 A-6 A-7 A-8 A-9 A-10 A-11 A-12
3.000 3.000 2.000 2.000 3.000 3.000 2.000 2.000 3.000 3.000 2.000 2.000
2.000 2.000 3.000 3.000 2.000 2.000 3.000 3.000 2.000 2.000 3.000 3.000
3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000
12.000 12.000 8.000 8.000 12.000 12.000 8.000 8.000 12.000 12.000 8.000 8.000
8.000 8.000 12.000 12.000 8.000 8.000 12.000 12.000 8.000 8.000 12.000 12.000
2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000
10 10 10 10 10 10 10 10 10 10 10 10
6 6 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6 6
4 4 4 4 4 4 4 4 4 4 4 4
12 12 12 12 12 12 12 12 12 12 12 12
0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008
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