"PILEGRP" --- PILE GROUP ANALYSIS PROGRAM Program Description: "PILEGRP" is a spreadsheet program written in MS-Excel for the purpose of analysis of pile caps using the "elastic method". Specifically, the properties of the pile group are calcul upon the applied vertical and horizontal loadings, the vertical and horizontal pile reactio There is also a worksheet to check beam and punching shear in the pile cap for a single cor purpose of estimating the required pile cap thickness and subsequent pile cap weight. This program is a workbook consisting of ten (10) worksheets, described as follows: Worksheet Name Description Doc This documentation sheet Piles (<=25) Pile group analysis for up to 25 total piles and 4 piers/lo Piles (<=25)(metric) le group analysis for up to 25 total piles and 4 piers/loading Piles (<=75) Pile group analysis for up to 75 total piles and 8 piers/lo Piles (<=75)(metric) le group analysis for up to 75 total piles and 8 piers/loading Piles (<=300) Pile group analysis for up to 300 total piles and 17 piers/l Piles (<=300)(metric) e group analysis for up to 300 total piles and 17 piers/loadin Piles (<=400) Pile group analysis for up to 400 total piles and 23 piers/l Piles (<=400)(metric) e group analysis for up to 400 total piles and 23 piers/loadin Corner Pile Shear Beam and punching shear checks for pile cap for single corne Program Assumptions and Limitations: 1. The Pile Group worksheets assume a minimum of 2 piles and a maximum of either 25, 75, 3 for a pile group. 2. This program uses the "elastic method" of analysis, assuming that the pile cap is in fa applied loads are linearly distributed among the piles. A common "rule-of-thumb" is t thickness equal to least 1/10 of the longest dimension (length or width) of the pile c to be vertical, and of equal size and length (stiffness). Battered piles are NOT perm are assumed at the same level. 3. This program assumes an orthogonal X-Y-Z coordinate system. All piles and piers MUST B "positive" (1st) quadrant. "Negative" pile or pier/loading location coordinates are N "Right-Hand-Rule" sign convention is used for all applied forces and moments at pier l 4. The piles and piers/loadings can be numbered in any desired order. However, the user s sure to either clear the contents of all spreadsheet cells that are not used for input be input = 0. All piles and piers/loadings MUST BE input in proper numerical sequence the numerical order of input data. 5. This program does NOT include the weight of the pile cap or piers in the calculation of However, the total weight of the pile cap and piers may be included by assuming an add located at the centroid of the pile cap plan area, and applying the total weight at th 6. This program does NOT check the actual calculated pile reactions (vertical and horizont or given allowable pile reactions for downward, uplift, or lateral cases. This is don acceptable overstress is left up to the judgement of the user. However, in all cases the user. 7. This program does NOT check the shear (beam-type or punching) nor the flexural requirem This must be done independently by the user. 8. This program contains numerous “comment boxes” which contain a wide variety of informat explanations of input or output items, equations used, data tables, etc. (Note: pres is denoted by a “red triangle” in the upper right-hand corner of a cell. Merely move
X-Coordinate (ft.) = S Hy =Y-Coordinate (ft.) = S Mx =
Dist. to T/Piles, h (ft.) = S My =Vertical Load, Pz (k) = S Mz =
Horiz. Load, Hx (k) = S Hy =Horiz. Load, Hy (k) =
Moment, Mx (ft-k) =Moment, My (ft-k) =Moment, Mz (ft-k) =
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
0.0
5.0
10.0
15.0
20.0
25.0 PILE GROUP PLAN
X - AXIS (ft.)Y
- A
XIS
(ft
.)
C9
The minimum number of piles = 2. The maximum number of piles = 25.
B11
The 'Xo' coordinate is the x-distance from the origin axis to a particular pile.
C11
The 'Yo' coordinate is the y-distance from the origin axis to a particular pile.
E11
The Vertical Pile Reaction, 'Rz', at each pile is calculated as follows: Rz = (-S Pz)/Np + ((S My)*Ix-(-S Mx)*Ixy)/(Ix*Iy-Ixy^2)*Xp + ((S Mx)*Iy-(S My)*Ixy)/(Ix*Iy-Ixy^2)*Yp where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Sign convention for 'Rz' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
F11
The Horizontal Pile Reaction, 'Rh', at each pile is calculated as follows: Rh = (((S Hx)/Np + (S Mz)*Yp/J)^2 + ((S Hy)/Np + (S Mz)*Xp/J)^2)^(1/2) where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Note: 'Rh' is an "absolute" value with no particular sign convention, thus no directional sense.
H30
The location of the centroidal Y-axis from the origin Y-axis is calculated as follows: Xc = S (Xo)/Np where: Np = total number of piles in group
H31
The location of the centroidal X-axis from the origin X-axis is calculated as follows: Yc = S (Yo)/Np where: Np = total number of piles in group
H32
The X-axis Moment of Inertia, 'Ix', for the pile group is calculated as follows: Ix = Ap*S (dy)^2 where: Ap = Area of pile assumed = unity (1) dy = y-distance of each pile from centroidal X-axis
H33
The Y-axis Moment of Inertia, 'Iy', for the pile group is calculated as follows: Iy = Ap*S (dx)^2 where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis
H34
The Polar Moment of Inertia for the pile group is calculated as follows: J = Ix+Iy
H35
The Product Moment of Inertia, 'Ixy', for the pile group is calculated as follows: Ixy = Ap*S (dx*dy) where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis dy = y-distance of each pile from centroidal X-axis Note: 'Ixy' = 0 for a pile group with at least one axis of symmetry.
H36
The orientation of the principal axes, is defined by the rotation angle, 'q ', from the centroidal axes and is calculated as follows: q = (ATAN(-2*Ixy/(Ix-Iy)))/2 Note: sign convention is positive (+) ccw. 'q ' = 0 for a pile group with at least one axis of symmetry.
H39
S Pz = sum of all applied vertical (Z-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Z-axis direction
B40
All piers must be located in the positive 1st quadrant. That is, all pier X, Y coordinate values must be >= 0. Note: The user should make sure to either clear the contents of all cells that are not used for input of pier coordinates, or those cell values should be input = 0.
H40
S Hx = sum of all applied horizontal (X-axis) loads translated to the centroid of the pile group. Sign convention: positive in +X-axis direction
B41
The 'X' coordinate is the x-distance from the origin axis to a particular pier/loading.
H41
S Hy = sum of all applied horizontal (Y-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Y-axis direction
B42
The 'Y' coordinate is the y-distance from the origin axis to a particular pier/loading.
H42
S Mx = sum of all applied X-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +X-axis
B43
The vertical distance, 'h', from the point of application of any horizontal loads (Hx, Hy) to the top of the piles. This 'h' distance should always be a positive number, but it may be input = 0 if there are no horizontal loads at that pier. The 'h' distance is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
H43
S My = sum of all applied Y-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Y-axis
B44
'Pz' is the vertical (Z-axis) load to be applied at the pier location. Sign convention: + = upward (out of page) - = downward (into page) for gravity loads
H44
S Mz = sum of all applied Z-axis moments translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Z-axis
B45
'Hx' is the horizontal (X-axis) load to be applied at the pier location. Sign convention: + = to right
B46
'Hy' is the horizontal (Y-axis) load to be applied at the pier location. Sign convention: + = up the page
B47
'Mx' is the X-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +X-axis
H47
Sign convention for 'Rz(max)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B48
'My' is the Y-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Y-axis
H48
Sign convention for 'Rz(min)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B49
'Mz' is the Z-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Z-axis
H49
Note: 'Rh(max)' is an "absolute" value with no particular sign convention, thus no directional sense.
"PILEGRP.xls" ProgramVersion 3.5
4 of 24 04/08/2023 06:19:33
PILE GROUP ANALYSIS FOR RIGID PILE CAPUsing the Elastic Method for up to 25 Total Piles
X-Coordinate (m) = S Hy =Y-Coordinate (m) = S Mx =
Dist. to T/Piles, h (m) = S My =Vertical Load, Pz (kN) = S Mz =
Horiz. Load, Hx (kN) = S Hy =Horiz. Load, Hy (kN) =Moment, Mx (kN-m) =Moment, My (kN-m) =Moment, Mz (kN-m) =
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0 PILE GROUP PLAN
X - AXIS (m)Y
- A
XIS
(m
)
C9
The minimum number of piles = 2. The maximum number of piles = 25.
B11
The 'Xo' coordinate is the x-distance from the origin axis to a particular pile.
C11
The 'Yo' coordinate is the y-distance from the origin axis to a particular pile.
E11
The Vertical Pile Reaction, 'Rz', at each pile is calculated as follows: Rz = (-S Pz)/Np + ((S My)*Ix-(-S Mx)*Ixy)/(Ix*Iy-Ixy^2)*Xp + ((S Mx)*Iy-(S My)*Ixy)/(Ix*Iy-Ixy^2)*Yp where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Sign convention for 'Rz' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
F11
The Horizontal Pile Reaction, 'Rh', at each pile is calculated as follows: Rh = (((S Hx)/Np + (S Mz)*Yp/J)^2 + ((S Hy)/Np + (S Mz)*Xp/J)^2)^(1/2) where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Note: 'Rh' is an "absolute" value with no particular sign convention, thus no directional sense.
H30
The location of the centroidal Y-axis from the origin Y-axis is calculated as follows: Xc = S (Xo)/Np where: Np = total number of piles in group
H31
The location of the centroidal X-axis from the origin X-axis is calculated as follows: Yc = S (Yo)/Np where: Np = total number of piles in group
H32
The X-axis Moment of Inertia, 'Ix', for the pile group is calculated as follows: Ix = Ap*S (dy)^2 where: Ap = Area of pile assumed = unity (1) dy = y-distance of each pile from centroidal X-axis
H33
The Y-axis Moment of Inertia, 'Iy', for the pile group is calculated as follows: Iy = Ap*S (dx)^2 where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis
H34
The Polar Moment of Inertia for the pile group is calculated as follows: J = Ix+Iy
H35
The Product Moment of Inertia, 'Ixy', for the pile group is calculated as follows: Ixy = Ap*S (dx*dy) where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis dy = y-distance of each pile from centroidal X-axis Note: 'Ixy' = 0 for a pile group with at least one axis of symmetry.
H36
The orientation of the principal axes, is defined by the rotation angle, 'q ', from the centroidal axes and is calculated as follows: q = (ATAN(-2*Ixy/(Ix-Iy)))/2 Note: sign convention is positive (+) ccw. 'q ' = 0 for a pile group with at least one axis of symmetry.
H39
S Pz = sum of all applied vertical (Z-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Z-axis direction
B40
All piers must be located in the positive 1st quadrant. That is, all pier X, Y coordinate values must be >= 0. Note: The user should make sure to either clear the contents of all cells that are not used for input of pier coordinates, or those cell values should be input = 0.
H40
S Hx = sum of all applied horizontal (X-axis) loads translated to the centroid of the pile group. Sign convention: positive in +X-axis direction
B41
The 'X' coordinate is the x-distance from the origin axis to a particular pier/loading.
H41
S Hy = sum of all applied horizontal (Y-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Y-axis direction
B42
The 'Y' coordinate is the y-distance from the origin axis to a particular pier/loading.
H42
S Mx = sum of all applied X-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +X-axis
B43
The vertical distance, 'h', from the point of application of any horizontal loads (Hx, Hy) to the top of the piles. This 'h' distance should always be a positive number, but it may be input = 0 if there are no horizontal loads at that pier. The 'h' distance is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
H43
S My = sum of all applied Y-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Y-axis
B44
'Pz' is the vertical (Z-axis) load to be applied at the pier location. Sign convention: + = upward (out of page) - = downward (into page) for gravity loads
H44
S Mz = sum of all applied Z-axis moments translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Z-axis
B45
'Hx' is the horizontal (X-axis) load to be applied at the pier location. Sign convention: + = to right
B46
'Hy' is the horizontal (Y-axis) load to be applied at the pier location. Sign convention: + = up the page
B47
'Mx' is the X-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +X-axis
H47
Sign convention for 'Rz(max)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B48
'My' is the Y-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Y-axis
H48
Sign convention for 'Rz(min)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B49
'Mz' is the Z-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Z-axis
H49
Note: 'Rh(max)' is an "absolute" value with no particular sign convention, thus no directional sense.
"PILEGRP.xls" ProgramVersion 3.5
5 of 24 04/08/2023 06:19:33
PILE GROUP ANALYSIS FOR RIGID PILE CAPUsing the Elastic Method for up to 75 Total Piles
(For English Units)Job Name: Subject: Pile No.:
Job Number: Originator: Checker: ######
Input Data: ######
Number of Piles, Np = 40 Pile Coordinates: Pile Coordinates: Pile Coodinates:
Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.)
X (ft.) =Y (ft.) =h (ft.) =
Pz (k) =Hx (k) =Hy (k) =
Mx (ft-k) =My (ft-k) =Mz (ft-k) =
C9
The minimum number of piles = 2. The maximum number of piles = 75.
B11
The 'Xo' coordinate is the x-distance from the origin axis to a particular pile.
C11
The 'Yo' coordinate is the y-distance from the origin axis to a particular pile.
A41
The 'X' coordinate is the x-distance from the origin axis to a particular pier/loading.
A42
The 'Y' coordinate is the y-distance from the origin axis to a particular pier/loading.
A43
The vertical distance, 'h', from the point of application of any horizontal loads (Hx, Hy) to the top of the piles. This 'h' distance should always be a positive number, but it may be input = 0 if there are no horizontal loads at that pier. The 'h' distance is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
A44
'Pz' is the vertical (Z-axis) load to be applied at the pier location. Sign convention: + = upward (out of page) - = downward (into page) for gravity loads
A45
'Hx' is the horizontal (X-axis) load to be applied at the pier location. Sign convention: + = to right
A46
'Hy' is the horizontal (Y-axis) load to be applied at the pier location. Sign convention: + = up the page
A47
'Mx' is the X-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +X-axis
A48
'My' is the Y-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Y-axis
A49
'Mz' is the Z-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Z-axis
"PILEGRP.xls" ProgramVersion 3.5
6 of 24 04/08/2023 06:19:33
(continued)
"PILEGRP.xls" ProgramVersion 3.5
7 of 24 04/08/2023 06:19:33
###Results: ###
Pile Group Properties: ###Xc = 4.500 ft. ###Yc = 13.500 ft. ###Ix = 2970.00 ft^2 ###Iy = 450.00 ft^2 ###J = 3420.00 ft^2 ###
The location of the centroidal Y-axis from the origin Y-axis is calculated as follows: Xc = S (Xo)/Np where: Np = total number of piles in group
B57
The location of the centroidal X-axis from the origin X-axis is calculated as follows: Yc = S (Yo)/Np where: Np = total number of piles in group
B58
The X-axis Moment of Inertia, 'Ix', for the pile group is calculated as follows: Ix = Ap*S (dy)^2 where: Ap = Area of pile assumed = unity (1) dy = y-distance of each pile from centroidal X-axis
B59
The Y-axis Moment of Inertia, 'Iy', for the pile group is calculated as follows: Iy = Ap*S (dx)^2 where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis
B60
The Polar Moment of Inertia for the pile group is calculated as follows: J = Ix+Iy
B61
The Product Moment of Inertia, 'Ixy', for the pile group is calculated as follows: Ixy = Ap*S (dx*dy) where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis dy = y-distance of each pile from centroidal X-axis Note: 'Ixy' = 0 for a pile group with at least one axis of symmetry.
B62
The orientation of the principal axes, is defined by the rotation angle, 'q ', from the centroidal axes and is calculated as follows: q = (ATAN(-2*Ixy/(Ix-Iy)))/2 Note: sign convention is positive (+) ccw. 'q ' = 0 for a pile group with at least one axis of symmetry.
B65
S Pz = sum of all applied vertical (Z-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Z-axis direction
B66
S Hx = sum of all applied horizontal (X-axis) loads translated to the centroid of the pile group. Sign convention: positive in +X-axis direction
B67
S Hy = sum of all applied horizontal (Y-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Y-axis direction
B68
S Mx = sum of all applied X-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +X-axis
B69
S My = sum of all applied Y-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Y-axis
B70
S Mz = sum of all applied Z-axis moments translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Z-axis
B73
The Vertical Pile Reaction, 'Rz', at each pile is calculated as follows: Rz = (-S Pz)/Np + ((S My)*Ix-(-S Mx)*Ixy)/(Ix*Iy-Ixy^2)*Xp + ((S Mx)*Iy-(S My)*Ixy)/(Ix*Iy-Ixy^2)*Yp where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Sign convention for 'Rz' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C73
The Horizontal Pile Reaction, 'Rh', at each pile is calculated as follows: Rh = (((S Hx)/Np + (S Mz)*Yp/J)^2 + ((S Hy)/Np + (S Mz)*Xp/J)^2)^(1/2) where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Note: 'Rh' is an "absolute" value with no particular sign convention, thus no directional sense.
C101
Sign convention for 'Rz(max)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C102
Sign convention for 'Rz(min)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C103
Note: 'Rh(max)' is an "absolute" value with no particular sign convention, thus no directional sense.
"PILEGRP.xls" ProgramVersion 3.5
8 of 24 04/08/2023 06:19:33
"PILEGRP.xls" ProgramVersion 3.5
9 of 24 04/08/2023 06:19:33
PILE GROUP ANALYSIS FOR RIGID PILE CAPUsing the Elastic Method for up to 75 Total Piles
(For Metric Units)Job Name: Subject: Pile No.:
Job Number: Originator: Checker: ######
Input Data: ######
Number of Piles, Np = 40 Pile Coordinates: Pile Coordinates: Pile Coodinates:
The minimum number of piles = 2. The maximum number of piles = 75.
B11
The 'Xo' coordinate is the x-distance from the origin axis to a particular pile.
C11
The 'Yo' coordinate is the y-distance from the origin axis to a particular pile.
A41
The 'X' coordinate is the x-distance from the origin axis to a particular pier/loading.
A42
The 'Y' coordinate is the y-distance from the origin axis to a particular pier/loading.
A43
The vertical distance, 'h', from the point of application of any horizontal loads (Hx, Hy) to the top of the piles. This 'h' distance should always be a positive number, but it may be input = 0 if there are no horizontal loads at that pier. The 'h' distance is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
A44
'Pz' is the vertical (Z-axis) load to be applied at the pier location. Sign convention: + = upward (out of page) - = downward (into page) for gravity loads
A45
'Hx' is the horizontal (X-axis) load to be applied at the pier location. Sign convention: + = to right
A46
'Hy' is the horizontal (Y-axis) load to be applied at the pier location. Sign convention: + = up the page
A47
'Mx' is the X-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +X-axis
A48
'My' is the Y-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Y-axis
A49
'Mz' is the Z-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Z-axis
"PILEGRP.xls" ProgramVersion 3.5
10 of 24 04/08/2023 06:19:33
(continued)
"PILEGRP.xls" ProgramVersion 3.5
11 of 24 04/08/2023 06:19:33
###Results: ###
Pile Group Properties: ###Xc = 1.372 m ###Yc = 4.115 m ###Ix = 275.92 m^2 ###Iy = 41.81 m^2 ###J = 317.73 m^2 ###
The location of the centroidal Y-axis from the origin Y-axis is calculated as follows: Xc = S (Xo)/Np where: Np = total number of piles in group
B57
The location of the centroidal X-axis from the origin X-axis is calculated as follows: Yc = S (Yo)/Np where: Np = total number of piles in group
B58
The X-axis Moment of Inertia, 'Ix', for the pile group is calculated as follows: Ix = Ap*S (dy)^2 where: Ap = Area of pile assumed = unity (1) dy = y-distance of each pile from centroidal X-axis
B59
The Y-axis Moment of Inertia, 'Iy', for the pile group is calculated as follows: Iy = Ap*S (dx)^2 where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis
B60
The Polar Moment of Inertia for the pile group is calculated as follows: J = Ix+Iy
B61
The Product Moment of Inertia, 'Ixy', for the pile group is calculated as follows: Ixy = Ap*S (dx*dy) where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis dy = y-distance of each pile from centroidal X-axis Note: 'Ixy' = 0 for a pile group with at least one axis of symmetry.
B62
The orientation of the principal axes, is defined by the rotation angle, 'q ', from the centroidal axes and is calculated as follows: q = (ATAN(-2*Ixy/(Ix-Iy)))/2 Note: sign convention is positive (+) ccw. 'q ' = 0 for a pile group with at least one axis of symmetry.
B65
S Pz = sum of all applied vertical (Z-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Z-axis direction
B66
S Hx = sum of all applied horizontal (X-axis) loads translated to the centroid of the pile group. Sign convention: positive in +X-axis direction
B67
S Hy = sum of all applied horizontal (Y-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Y-axis direction
B68
S Mx = sum of all applied X-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +X-axis
B69
S My = sum of all applied Y-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Y-axis
B70
S Mz = sum of all applied Z-axis moments translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Z-axis
B73
The Vertical Pile Reaction, 'Rz', at each pile is calculated as follows: Rz = (-S Pz)/Np + ((S My)*Ix-(-S Mx)*Ixy)/(Ix*Iy-Ixy^2)*Xp + ((S Mx)*Iy-(S My)*Ixy)/(Ix*Iy-Ixy^2)*Yp where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Sign convention for 'Rz' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C73
The Horizontal Pile Reaction, 'Rh', at each pile is calculated as follows: Rh = (((S Hx)/Np + (S Mz)*Yp/J)^2 + ((S Hy)/Np + (S Mz)*Xp/J)^2)^(1/2) where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Note: 'Rh' is an "absolute" value with no particular sign convention, thus no directional sense.
C101
Sign convention for 'Rz(max)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C102
Sign convention for 'Rz(min)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C103
Note: 'Rh(max)' is an "absolute" value with no particular sign convention, thus no directional sense.
"PILEGRP.xls" ProgramVersion 3.5
12 of 24 04/08/2023 06:19:33
"PILEGRP.xls" ProgramVersion 3.5
13 of 24 04/08/2023 06:19:33
PILE GROUP ANALYSIS FOR RIGID PILE CAP CALCULATIONS:Using the Elastic Method for up to 300 Total Piles
(For English Units) Pile Dist. to X,Y axis:Job Name: Subject: Pile No.:
Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.)
X (ft.) =Y (ft.) =h (ft.) =
Pz (k) =Hx (k) =Hy (k) =
Mx (ft-k) =My (ft-k) =Mz (ft-k) =
S Loads @ C.G. of Pile Group:S Pz =S Hx =S Hy =S Mx =S My =S Mz =
q =
C9
The minimum number of piles = 2. The maximum number of piles = 300.
B12
The 'Xo' coordinate is the x-distance from the origin axis to a particular pile.
C12
The 'Yo' coordinate is the y-distance from the origin axis to a particular pile.
A67
The 'X' coordinate is the x-distance from the origin axis to a particular pier/loading.
A68
The 'Y' coordinate is the y-distance from the origin axis to a particular pier/loading.
A69
The vertical distance, 'h', from the point of application of any horizontal loads (Hx, Hy) to the top of the piles. This 'h' distance should always be a positive number, but it may be input = 0 if there are no horizontal loads at that pier. The 'h' distance is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
A70
'Pz' is the vertical (Z-axis) load to be applied at the pier location. Sign convention: + = upward (out of page) - = downward (into page) for gravity loads
A71
'Hx' is the horizontal (X-axis) load to be applied at the pier location. Sign convention: + = to right
A72
'Hy' is the horizontal (Y-axis) load to be applied at the pier location. Sign convention: + = up the page
A73
'Mx' is the X-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +X-axis
A74
'My' is the Y-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Y-axis
A75
'Mz' is the Z-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Z-axis
B82
The location of the centroidal Y-axis from the origin Y-axis is calculated as follows: Xc = S (Xo)/Np where: Np = total number of piles in group
F82
S Pz = sum of all applied vertical (Z-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Z-axis direction
B83
The location of the centroidal X-axis from the origin X-axis is calculated as follows: Yc = S (Yo)/Np where: Np = total number of piles in group
F83
S Hx = sum of all applied horizontal (X-axis) loads translated to the centroid of the pile group. Sign convention: positive in +X-axis direction
B84
The X-axis Moment of Inertia, 'Ix', for the pile group is calculated as follows: Ix = Ap*S (dy)^2 where: Ap = Area of pile assumed = unity (1) dy = y-distance of each pile from centroidal X-axis
F84
S Hy = sum of all applied horizontal (Y-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Y-axis direction
B85
The Y-axis Moment of Inertia, 'Iy', for the pile group is calculated as follows: Iy = Ap*S (dx)^2 where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis
F85
S Mx = sum of all applied X-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +X-axis
B86
The Polar Moment of Inertia for the pile group is calculated as follows: J = Ix+Iy
F86
S My = sum of all applied Y-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Y-axis
B87
The Product Moment of Inertia, 'Ixy', for the pile group is calculated as follows: Ixy = Ap*S (dx*dy) where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis dy = y-distance of each pile from centroidal X-axis Note: 'Ixy' = 0 for a pile group with at least one axis of symmetry.
F87
S Mz = sum of all applied Z-axis moments translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Z-axis
B88
The orientation of the principal axes, is defined by the rotation angle, 'q ', from the centroidal axes and is calculated as follows: q = (ATAN(-2*Ixy/(Ix-Iy)))/2 Note: sign convention is positive (+) ccw. 'q ' = 0 for a pile group with at least one axis of symmetry.
B91
Sign convention for 'Rz(max)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B92
Sign convention for 'Rz(min)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B93
Note: 'Rh(max)' is an "absolute" value with no particular sign convention, thus no directional sense.
The Vertical Pile Reaction, 'Rz', at each pile is calculated as follows: Rz = (-S Pz)/Np + ((S My)*Ix-(-S Mx)*Ixy)/(Ix*Iy-Ixy^2)*Xp + ((S Mx)*Iy-(S My)*Ixy)/(Ix*Iy-Ixy^2)*Yp where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Sign convention for 'Rz' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C142
The Horizontal Pile Reaction, 'Rh', at each pile is calculated as follows: Rh = (((S Hx)/Np + (S Mz)*Yp/J)^2 + ((S Hy)/Np + (S Mz)*Xp/J)^2)^(1/2) where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Note: 'Rh' is an "absolute" value with no particular sign convention, thus no directional sense.
"PILEGRP.xls" ProgramVersion 3.5
15 of 24 04/08/2023 06:19:33
PILE GROUP ANALYSIS FOR RIGID PILE CAP CALCULATIONS:Using the Elastic Method for up to 300 Total Piles
Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m)
X (m) =Y (m) =h (m) =
Pz (kN) =Hx (kN) =Hy (kN) =
Mx (kN-m) =My (kN-m) =Mz (kN-m) =
S Loads @ C.G. of Pile Group:S Pz =S Hx =S Hy =S Mx =S My =S Mz =
q =
C9
The minimum number of piles = 2. The maximum number of piles = 300.
B12
The 'Xo' coordinate is the x-distance from the origin axis to a particular pile.
C12
The 'Yo' coordinate is the y-distance from the origin axis to a particular pile.
A67
The 'X' coordinate is the x-distance from the origin axis to a particular pier/loading.
A68
The 'Y' coordinate is the y-distance from the origin axis to a particular pier/loading.
A69
The vertical distance, 'h', from the point of application of any horizontal loads (Hx, Hy) to the top of the piles. This 'h' distance should always be a positive number, but it may be input = 0 if there are no horizontal loads at that pier. The 'h' distance is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
A70
'Pz' is the vertical (Z-axis) load to be applied at the pier location. Sign convention: + = upward (out of page) - = downward (into page) for gravity loads
A71
'Hx' is the horizontal (X-axis) load to be applied at the pier location. Sign convention: + = to right
A72
'Hy' is the horizontal (Y-axis) load to be applied at the pier location. Sign convention: + = up the page
A73
'Mx' is the X-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +X-axis
A74
'My' is the Y-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Y-axis
A75
'Mz' is the Z-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Z-axis
B82
The location of the centroidal Y-axis from the origin Y-axis is calculated as follows: Xc = S (Xo)/Np where: Np = total number of piles in group
F82
S Pz = sum of all applied vertical (Z-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Z-axis direction
B83
The location of the centroidal X-axis from the origin X-axis is calculated as follows: Yc = S (Yo)/Np where: Np = total number of piles in group
F83
S Hx = sum of all applied horizontal (X-axis) loads translated to the centroid of the pile group. Sign convention: positive in +X-axis direction
B84
The X-axis Moment of Inertia, 'Ix', for the pile group is calculated as follows: Ix = Ap*S (dy)^2 where: Ap = Area of pile assumed = unity (1) dy = y-distance of each pile from centroidal X-axis
F84
S Hy = sum of all applied horizontal (Y-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Y-axis direction
B85
The Y-axis Moment of Inertia, 'Iy', for the pile group is calculated as follows: Iy = Ap*S (dx)^2 where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis
F85
S Mx = sum of all applied X-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +X-axis
B86
The Polar Moment of Inertia for the pile group is calculated as follows: J = Ix+Iy
F86
S My = sum of all applied Y-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Y-axis
B87
The Product Moment of Inertia, 'Ixy', for the pile group is calculated as follows: Ixy = Ap*S (dx*dy) where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis dy = y-distance of each pile from centroidal X-axis Note: 'Ixy' = 0 for a pile group with at least one axis of symmetry.
F87
S Mz = sum of all applied Z-axis moments translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Z-axis
B88
The orientation of the principal axes, is defined by the rotation angle, 'q ', from the centroidal axes and is calculated as follows: q = (ATAN(-2*Ixy/(Ix-Iy)))/2 Note: sign convention is positive (+) ccw. 'q ' = 0 for a pile group with at least one axis of symmetry.
B91
Sign convention for 'Rz(max)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B92
Sign convention for 'Rz(min)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B93
Note: 'Rh(max)' is an "absolute" value with no particular sign convention, thus no directional sense.
The Vertical Pile Reaction, 'Rz', at each pile is calculated as follows: Rz = (-S Pz)/Np + ((S My)*Ix-(-S Mx)*Ixy)/(Ix*Iy-Ixy^2)*Xp + ((S Mx)*Iy-(S My)*Ixy)/(Ix*Iy-Ixy^2)*Yp where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Sign convention for 'Rz' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C142
The Horizontal Pile Reaction, 'Rh', at each pile is calculated as follows: Rh = (((S Hx)/Np + (S Mz)*Yp/J)^2 + ((S Hy)/Np + (S Mz)*Xp/J)^2)^(1/2) where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Note: 'Rh' is an "absolute" value with no particular sign convention, thus no directional sense.
"PILEGRP.xls" ProgramVersion 3.5
17 of 24 04/08/2023 06:19:33
PILE GROUP ANALYSIS FOR RIGID PILE CAP CALCULATIONS:Using the Elastic Method for up to 400 Total Piles
(For English Units) Pile Dist. to X,Y axis:Job Name: Subject: Pile No.:
Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.) Xo (ft.) Yo (ft.)
X (ft.) =Y (ft.) =h (ft.) =
Pz (k) =Hx (k) =Hy (k) =
Mx (ft-k) =My (ft-k) =Mz (ft-k) =
C9
The minimum number of piles = 2. The maximum number of piles = 400.
B12
The 'Xo' coordinate is the x-distance from the origin axis to a particular pile.
C12
The 'Yo' coordinate is the y-distance from the origin axis to a particular pile.
A67
The 'X' coordinate is the x-distance from the origin axis to a particular pier/loading.
A68
The 'Y' coordinate is the y-distance from the origin axis to a particular pier/loading.
A69
The vertical distance, 'h', from the point of application of any horizontal loads (Hx, Hy) to the top of the piles. This 'h' distance should always be a positive number, but it may be input = 0 if there are no horizontal loads at that pier. The 'h' distance is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
A70
'Pz' is the vertical (Z-axis) load to be applied at the pier location. Sign convention: + = upward (out of page) - = downward (into page) for gravity loads
A71
'Hx' is the horizontal (X-axis) load to be applied at the pier location. Sign convention: + = to right
A72
'Hy' is the horizontal (Y-axis) load to be applied at the pier location. Sign convention: + = up the page
A73
'Mx' is the X-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +X-axis
A74
'My' is the Y-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Y-axis
A75
'Mz' is the Z-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Z-axis
The location of the centroidal Y-axis from the origin Y-axis is calculated as follows: Xc = S (Xo)/Np where: Np = total number of piles in group
E160
S Pz = sum of all applied vertical (Z-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Z-axis direction
B161
The location of the centroidal X-axis from the origin X-axis is calculated as follows: Yc = S (Yo)/Np where: Np = total number of piles in group
E161
S Hx = sum of all applied horizontal (X-axis) loads translated to the centroid of the pile group. Sign convention: positive in +X-axis direction
B162
The X-axis Moment of Inertia, 'Ix', for the pile group is calculated as follows: Ix = Ap*S (dy)^2 where: Ap = Area of pile assumed = unity (1) dy = y-distance of each pile from centroidal X-axis
E162
S Hy = sum of all applied horizontal (Y-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Y-axis direction
B163
The Y-axis Moment of Inertia, 'Iy', for the pile group is calculated as follows: Iy = Ap*S (dx)^2 where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis
E163
S Mx = sum of all applied X-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +X-axis
B164
The Polar Moment of Inertia for the pile group is calculated as follows: J = Ix+Iy
E164
S My = sum of all applied Y-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Y-axis
B165
The Product Moment of Inertia, 'Ixy', for the pile group is calculated as follows: Ixy = Ap*S (dx*dy) where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis dy = y-distance of each pile from centroidal X-axis Note: 'Ixy' = 0 for a pile group with at least one axis of symmetry.
E165
S Mz = sum of all applied Z-axis moments translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Z-axis
B166
The orientation of the principal axes, is defined by the rotation angle, 'q ', from the centroidal axes and is calculated as follows: q = (ATAN(-2*Ixy/(Ix-Iy)))/2 Note: sign convention is positive (+) ccw. 'q ' = 0 for a pile group with at least one axis of symmetry.
B170
Sign convention for 'Rz(max)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B171
Sign convention for 'Rz(min)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B172
Note: 'Rh(max)' is an "absolute" value with no particular sign convention, thus no directional sense.
B179
The Vertical Pile Reaction, 'Rz', at each pile is calculated as follows: Rz = (-S Pz)/Np + ((S My)*Ix-(-S Mx)*Ixy)/(Ix*Iy-Ixy^2)*Xp + ((S Mx)*Iy-(S My)*Ixy)/(Ix*Iy-Ixy^2)*Yp where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Sign convention for 'Rz' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C179
The Horizontal Pile Reaction, 'Rh', at each pile is calculated as follows: Rh = (((S Hx)/Np + (S Mz)*Yp/J)^2 + ((S Hy)/Np + (S Mz)*Xp/J)^2)^(1/2) where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Note: 'Rh' is an "absolute" value with no particular sign convention, thus no directional sense.
"PILEGRP.xls" ProgramVersion 3.5
20 of 24 04/08/2023 06:19:33
PILE GROUP ANALYSIS FOR RIGID PILE CAP CALCULATIONS:Using the Elastic Method for up to 400 Total Piles
Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m) Xo (m) Yo (m)
C9
The minimum number of piles = 2. The maximum number of piles = 400.
B12
The 'Xo' coordinate is the x-distance from the origin axis to a particular pile.
C12
The 'Yo' coordinate is the y-distance from the origin axis to a particular pile.
A67
The 'X' coordinate is the x-distance from the origin axis to a particular pier/loading.
A68
The 'Y' coordinate is the y-distance from the origin axis to a particular pier/loading.
A69
The vertical distance, 'h', from the point of application of any horizontal loads (Hx, Hy) to the top of the piles. This 'h' distance should always be a positive number, but it may be input = 0 if there are no horizontal loads at that pier. The 'h' distance is used in conjunction with the horizontal loads to obtain any additional moments (Mx, My) that are to be eventually summed with the applied moments.
A70
'Pz' is the vertical (Z-axis) load to be applied at the pier location. Sign convention: + = upward (out of page) - = downward (into page) for gravity loads
A71
'Hx' is the horizontal (X-axis) load to be applied at the pier location. Sign convention: + = to right
A72
'Hy' is the horizontal (Y-axis) load to be applied at the pier location. Sign convention: + = up the page
A73
'Mx' is the X-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +X-axis
A74
'My' is the Y-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Y-axis
A75
'Mz' is the Z-axis moment to be applied at the pier location. Sign convention: + = by "Right-Hand-Rule" about +Z-axis
The location of the centroidal Y-axis from the origin Y-axis is calculated as follows: Xc = S (Xo)/Np where: Np = total number of piles in group
E160
S Pz = sum of all applied vertical (Z-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Z-axis direction
B161
The location of the centroidal X-axis from the origin X-axis is calculated as follows: Yc = S (Yo)/Np where: Np = total number of piles in group
E161
S Hx = sum of all applied horizontal (X-axis) loads translated to the centroid of the pile group. Sign convention: positive in +X-axis direction
B162
The X-axis Moment of Inertia, 'Ix', for the pile group is calculated as follows: Ix = Ap*S (dy)^2 where: Ap = Area of pile assumed = unity (1) dy = y-distance of each pile from centroidal X-axis
E162
S Hy = sum of all applied horizontal (Y-axis) loads translated to the centroid of the pile group. Sign convention: positive in +Y-axis direction
B163
The Y-axis Moment of Inertia, 'Iy', for the pile group is calculated as follows: Iy = Ap*S (dx)^2 where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis
E163
S Mx = sum of all applied X-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +X-axis
B164
The Polar Moment of Inertia for the pile group is calculated as follows: J = Ix+Iy
E164
S My = sum of all applied Y-axis moments calculated at the top of the piles and translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Y-axis
B165
The Product Moment of Inertia, 'Ixy', for the pile group is calculated as follows: Ixy = Ap*S (dx*dy) where: Ap = Area of pile assumed = unity (1) dx = x-distance of each pile from centroidal Y-axis dy = y-distance of each pile from centroidal X-axis Note: 'Ixy' = 0 for a pile group with at least one axis of symmetry.
E165
S Mz = sum of all applied Z-axis moments translated to the centroid of the pile group. Sign convention: positive by "Right-Hand-Rule" about +Z-axis
B166
The orientation of the principal axes, is defined by the rotation angle, 'q ', from the centroidal axes and is calculated as follows: q = (ATAN(-2*Ixy/(Ix-Iy)))/2 Note: sign convention is positive (+) ccw. 'q ' = 0 for a pile group with at least one axis of symmetry.
B170
Sign convention for 'Rz(max)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B171
Sign convention for 'Rz(min)' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
B172
Note: 'Rh(max)' is an "absolute" value with no particular sign convention, thus no directional sense.
B179
The Vertical Pile Reaction, 'Rz', at each pile is calculated as follows: Rz = (-S Pz)/Np + ((S My)*Ix-(-S Mx)*Ixy)/(Ix*Iy-Ixy^2)*Xp + ((S Mx)*Iy-(S My)*Ixy)/(Ix*Iy-Ixy^2)*Yp where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Sign convention for 'Rz' is as follows: positive (+) = compression pile reaction negative (-) = tension (uplift) pile reaction
C179
The Horizontal Pile Reaction, 'Rh', at each pile is calculated as follows: Rh = (((S Hx)/Np + (S Mz)*Yp/J)^2 + ((S Hy)/Np + (S Mz)*Xp/J)^2)^(1/2) where: Xp = x-distance of pile from centroidal Y-axis Yp = y-distance of pile from centroidal X-axis Note: 'Rh' is an "absolute" value with no particular sign convention, thus no directional sense.
"PILEGRP.xls" ProgramVersion 3.5
23 of 24 04/08/2023 06:19:33
BEAM AND PUNCHING SHEAR CHECKS FOR PILE CAPfor Single Corner PilePer ACI 318-99 Code
Job Name: Subject: YesJob Number: Originator: Checker: No
CS =Input: b =
E=18'' Vu =Pile Reaction, Rp = 140.00 kips
Pile Dia., Dp = 12.000 in. For Two-way, Punching Shear:Pile Edge Dist., E = 18.000 in. d =
Pile Spacing, L = 48.000 in. Dp=12'' CS =Pile Embedment, dp = 6.000 in. (L-Dp)/2=18'' E=18''
Pile Cap Thk, H = 36.000 in. Vu =Conc. Strength, f 'c = 3000.0 psi
Top Face Reinf.? Yes Dp/2=6''
USD Load Factor, LF = 1.6 d/2=13''
bo=65.845''
Nomenclature b=98.912''
Results:
For One-way, Beam Shear: Critical Section @ min. of d or (L-Dp)/2 from face of pilePile Cap Eff. Depth, d = 26.000 in. d = H-dp-4'' (Assume 4'' from top face to centroid of reinf.)
Critical Section, CS = 18.000 in. CS = minimum of: d or (L-Dp)/2Shear Width, b = 98.912 in. b = 2*(SQRT(2*E^2)+Dp/2+CS)
Ultimate Shear, Vu = 224.00 kips Vu = LF*Rp239.46 kips
Vu <= Allow. Shear, O.K.
For Two-way, Punching Shear: Critical Section @ min. of d/2 or (L-Dp)/2 from face of pilePile Cap Eff. Depth, d = 26.000 in. d = H-dp-4'' (Assume 4'' from top face to centroid of reinf.)
Critical Section, CS = 13.000 in. CS = minimum of: d/2 or (L-Dp)/2Shear Perimeter, bo = 65.845 in.
Ultimate Shear, Vu = 224.00 kips Vu = LF*Rp318.81 kips
Note: one-way, beam and two-way, punching shear checks for critical sections relative to pier(s) must also be performed. Checks for one-way deep beam and two-way deep corbel shear should also be considered.
C11
Suggested minimum pile edge distance, 'E', based on pile compression capacity is as follows: E = 15" for Rp <= 120 kips E = 21" for 120 kips < Rp <= 240 kips E = 27" for 240 kips < Rp <= 400 kips E = 30" for Rp > 400 kips
C13
Typical values of min. pile embedment, 'dp', are: dp = 6" for steel piles dp = 4" for concrete piles.
I29
Critical section for one-way, beam shear is limited to minimum of "d" or "(L-Dp)/2" so that there is no overlapping of critical sections from other piles.
I38
Critical section for two-way, punching shear is limited to minimum of "d/2" or "(L-Dp)/2" so that there is no overlapping of critical sections from other piles.
C41
Shear perimeter, 'bo', for defining critical section for two-way, punching shear is limited to a maximum value = 2*p*(Dp/2+CS).
![[XLS]'PILEGRP' Program - CALCULATOR EDGE · Web viewThis program does NOT include the weight of the pile cap or piers in the calculation of the vertical pile reactions. 6. This program](https://img.pdfslide.us/doc/110x75/5aca416d7f8b9a42358dc392/xlspilegrp-program-calculator-viewthis-program-does-not-include-the-weight.jpg)
