Bolt Group | Formulize

Calculation performs the analysis of the in-plane eccentric load using Elastic Method and is applied to various numbers of bolts in unconstraint arrangement. The applied load is translated to the centroid of the pattern and the resultant forces are then resolved into shear forces at individual bolt areas.

Assumptions

The following assumptions are considered in analysis:

The plate has the constant E and cross-section.

All bolts are assumed to have the same material and strength.

Moments are assumed to rotate the pattern about its centroid.

All loads are assumed to be at ULS and no factors are applied.

Limitations

The calculation has the following limitations:

Loads entered are applied in 2D plane on a bolt group.

Steel bolt diameters and grade are selectable from dropdown.

Number of applied loads F is limited to 1. In case of multiple loads acting at the bolt group at the same time the resultant forces should be add together.

Maximum number of bolts is limited to 20 in analysis in any geometrical arrangement.

Input Variables

The following input variables can be specified in the form.

Symbol	Description	Units	Limits
Bolt_x	Bolt coordinate X	mm / in	0 ≤ x ≤ 9999
Bolt_y	Bolt coordinate Y	mm / in	0 ≤ x ≤ 9999
Load_x	Loading point coordinate X	mm / in	0 ≤ x ≤ 9999
Load_y	Loading point coordinate Y	mm / in	0 ≤ x ≤ 9999
Load_z	Loading point coordinate Z	mm / in	-9999 ≤ x ≤ 9999
P_z	Axial force Pz	kN / kips	-9999 ≤ x ≤ 9999
P_x	Shear force Px	kN / kips	-9999 ≤ x ≤ 9999
P_y	Shear force Py	kN / kips	-9999 ≤ x ≤ 9999
M_x	Moment about X axis	kNm / kip-in	-9999 ≤ x ≤ 9999
M_y	Moment about Y axis	kNm / kip-in	-9999 ≤ x ≤ 9999
M_z	Moment about Z axis	kNm / kip-in	-9999 ≤ x ≤ 9999

Result Variables

The results are categorized and resultant tables are shown for easy navigation. Result variables are shown below.

Symbol	Description	Units
Centroid_x	Bolt group centroid X coordinate	mm / in
Centroid_y	Bolt group centroid Y coordinate	mm / in
∑ I_x	Sum of moments of inertia about the X-axis	mm² / in²
∑ I_y	Sum of moments of inertia about the Y-axis	mm² / in²
J	Polar moment of inertia	mm² / in²
∑ I_xy	Product of inertia	mm² / in²
θ	Angle of principal axes	°
∑ P_z	Sum of axial loads Pz at centroid	kN / kips
∑ P_x	Sum of shear loads Px at centroid	kN / kips
∑ P_y	Sum of shear loads Py at centroid	kN / kips
∑ M_z	Sum of moment loads Mz at centroid	kNm / kip-in
∑ M_x	Sum of moment loads Mx at centroid	kNm / kip-in
∑ M_y	Sum of moment loads My at centroid	kNm / kip-in
d_l,x	Distance in X from applied load to centroid of bolt group	mm / in
d_l,y	Distance in Y from applied load to centroid of bolt group	mm / in
M_xP_z	Moment about X axis from applied axial load Pz	kNm / kip-in
M_yP_z	Moment about Y axis from applied axial load Pz	kNm / kip-in
M_xP_y	Moment about X axis from applied shear load Py	kNm / kip-in
M_yP_x	Moment about Y axis from applied shear load Px	kNm / kip-in
M_zP_x	Moment about Z axis from applied shear load Px	kNm / kip-in
M_zP_y	Moment about Z axis from applied shear load Py	kNm / kip-in
d_b,x	Distance in X from bolt to centroid of bolt group	mm / in
d_b,y	Distance in Y from bolt to centroid of bolt group	mm / in
R_z	Bolt axial reaction in Z axis	kN / kips
R_x	Bolt reaction in X axis	kN / kips
R_y	Bolt reaction in Y axis	kN / kips
R_h	Bolt resultant horizontal reaction (Rx and Ry)	kN / kips

Standards

None

References

- Ruby, David I., All About Bolts, Modern Steel Construction, May 2003
- Salmon, C.G., Johnston, J.E., Steel Structures: Design & Behavior, 4th edition, HarperCollins, 1996

Release Date	Version	Description
January 2024	1.0.0	Initial release.

Bolt #	X [mm]	Y [mm]
B1	200	0
B2	600	0
B3	1000	0
B4	200	400
B5	600	400
B6	1000	400

Load #	X [mm]	Y [mm]	Z [mm]	Pz [kN]	Px [kN]	Py [kN]	Mx [kNm]	My [kNm]	Mz [kNm]
F1	100	200	0	25.00	45.40	12.50	7.50	11.50	18.50
F2	400	200	26	4.50	-2.50	14.50	32.50	17.50	8.50
F3	800	250	26	-74.50	29.50	-44.50	32.50	17.50	8.50
F4	1000	150	26	7.50	-92.50	-74.50	32.50	17.50	8.50