# FOOTINGS.xlsx

### Description

Program Description:

'FOOTINGS' is a spreadsheet program written in MS-Excel for the purpose of analysis of rigid rectangular spread footings with up to 16 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. There are also separate worksheets for the analysis of unsymetrical footings and octagonal footings.

This program is a workbook consisting of eight (8) worksheets, described as follows:

Worksheet Name - Description

Doc - Documentation sheet

Footing (8 net pier loads) - Individual rectangular spread footing analysis (with up to 8 net pier loadings)

Footing (16 net pier loads) - Individual rectangular spread footing analysis (with up to 16 net pier loadings)

Footing (breakdown of loads) - Individual rectangular spread footing analysis (with breakdown of loadings)

Unsymmetrical Footing Base - Unsymmetrical rigid footing base bearing pressure analysis

Octagonal Footing - Octagonal spread footing analysis

Footings (Table) - Multiple rectangular spread footings analysis and design (table format)

Footings (Pier Table) - Multiple rectangular spread footings - pier analysis (table format)

Program Assumptions and Limitations:

- This program assumes that the spread footing is in fact 'rigid', so that the bearing pressure is distributed linearly on a homogeneous soil. (Note: the actual footing is generally not 'rigid', nor is the pressure beneath it distributed linearly. However, it has been found that solutions using the assumed 'rigid' concept are adequate and generally result in a conservative design.)
- This program assumes an orthogonal X-Y-Z coordinate system with the origin located at the centroid of the footing in plan (footprint). 'Right-Hand-Rule' sign convention is used for input of all pier coordinates as well as for all applied forces and moments at piers.
- This program can handle from 1 up to either eight (8) or sixteen (16) total piers located anywhere on the base of the footing. Piers can be numbered in any desired order.
- This program does not check the actual calculated soil bearing pressure against a given allowable soil pressure. This is done so that the extent of acceptable overstress is left up to the judgment of the user. However, in all cases this must be checked by the user.
- This program does not use a specified permissible value for the factor of safety against overturning. However, a minimum value of 1.5 to 2.0 is suggested, based upon the particular conditions. (A 'Footing is unstable!' error message will be displayed if the factor of safety against overturning is 1.0. Then the user must revise the footing dimensions or other parameters.)
- This program does not use a specified permissible value for the factor of safety against uplift. However, a minimum value of 1.2 to 1.5 is suggested, based upon the particular conditions and the extent of footing confinement. (A 'Footing is unstable!' error message will be displayed if the factor of safety against uplift is 1.0. Then the user must revise the footing dimensions or other parameters.)
- The 'Footing (net pier loads)' worksheets deal with net applied loadings at the piers. That is, there is no allowance for individual breakdown of dead, live, and wind (or seismic) loadings. This worksheet should be specifically used in any of the following conditions:
- When the individual breakdown of loadings is not known or is not critical
- When there are little or no uplift or overturning forces and moments due to wind (or seismic)
- When the factor of safety against uplift or overturning due to wind (or seismic) is NOT critical
- When there are overturning forces or moments due to only gravity (dead or live) loadings
- The 'Footing (net pier loads)' worksheets consider all net applied moments and horizontal loads as forces causing overturning. However, a net uplift load is considered as a force causing overturning only when there is an applicable resultant eccentricity in the direction of overturning. For a net uplift pier load, the 'excess' pier weight (pier weight less soil weight) is subtracted from the net uplift load at the pier location.
- The 'Footing (breakdown of loads)' worksheet allows for individual breakdown of dead, live, and wind (or seismic) loadings. This worksheet should be specifically used in any of the following conditions:
- When the individual breakdown of loadings is known or is critical
- When there are uplift or overturning forces and moments due to wind (or seismic)
- When the factor of safety against uplift or overturning due to wind (or seismic) is critical
- When there are no overturning forces or moments due to only gravity (dead or live) loadings
- 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.
- 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.
- 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

- 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)

- 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

- The 'Unsymmetrical Footing Base' worksheet can aid the user with analysis of maximum soil pressure for situations where a non-rectangular shaped rigid footing base has to be used.
- The 'Octagonal Footing' worksheet can aid the user with analysis of the soil pressures and stability checks for octagonal shaped rigid footing with an octagonal shaped pier.
- 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.
- The 'Footings (Table)' and 'Footings (Pier Table)' worksheets enable the user to select either the ACI 318-99, 318-02, 318-05, 318-08, or 318-11 Code to perform the reinforced concrete analysis/design for one-way (beam-type) shear, two-way (punching) shear, and flexural reinforcing requirements.
- In the 'Footings (Table)' worksheet, the program assumes a 'tension controlled' section and uses f = 0.90 to determine required reinforcing. This is appropriate for the ACI 318-99 Code with applicable load factors. However, for either the ACI 318-02, 318-05, 318-08, or 318-11 Codes, f must be determined based on actual reinforcing used. If f 0.90 then the footing thickness will need to be increased until the calculated value of f is = 0.90 in order to use reinforcing results determined from this program.
- In the 'Footings (Pier Table)' worksheet, for pure flexure (no axial load) the program determines the strain in the tension reinforcing and then the capacity reduction factor f = 0.90.
- 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'.)

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