Machine Screws | Thread Shear

	Thread Shear
	Date:


Notes

1. An external thread refers to a bolt, screw or threaded rod.
2. An internal thread refers to a nut or tapped hole.
3. A factor of safety of at least 2 is recommended.

Factor of Safety

FS			safety factor


Engagment

L_e		mm	engagement length

Thread Designation
Des			thread designation
d		mm	basic thread diameter
p		mm	thread pitch

External Thread Class
M_E			external thread (screw) material
G_p			pitch diameter tolerance grade
G_d			major diameter tolerance grade
T_pos			tolerance position

Internal Thread Class
M_I			interal thread material
G_P			pitch diameter tolerance grade
G_D			minor diameter tolerance grade
T_POS			tolerance position

External Thread (Screw / Bolt) Properties
σ_{t_E}		MPa	minimum ultimate tensile strength
d_min		mm	minimum major diameter
d₁		mm	basic minor diameter
d₂		mm	basic pitch diameter
d_{2_min}		mm	minimum pitch diameter
w₂		mm	pitch diameter width
w_E		mm	base width of external thread
c_E		mm	circumference per revolution at D_{2_max}
s_E		mm	arc length per revolution at D_{2_max}
A_t		mm²	tensile area
A_s,c		mm²	thread shear area based on c_E
A_s,s		mm²	thread shear area based on s_E

Internal Thread (Nut / Tapped Hole) Properties
σ_{t_I}		MPa	minimum ultimate tensile strength
D_{1_max}		mm	maximum minor diameter
D_{2_max}		mm	maximum pitch diameter
w_I		mm	base width of internal thread
c_I		mm	circumference per revolution at d_min
s_I		mm	arc length per revolution at d_min
A_n,c		mm²	thread shear area based on c_I
A_n,s		mm²	thread shear area based on s_I

Limits

F_b		N	axial force required to break the bolt
F_{s_E}		N	axial force required to shear the external thread
F_{s_I}		N	axial force required to shear the internal thread
F_max		N	maximum allowable force to avoid thread shear
F_R		N	recommended allowable force based on FS

Directions

This calculator is designed to resemble a spreadsheet calculator that can be printed as a report for project recordkeeping. The term project, with regards to Precision Mindset calculators, refers to engineered designs, homework problems, tutorial problems, hobby designs or self-study.

Cells with a border are inputs and cells without a border are outputs. An external thread refers to a bolt, screw, or threaded rod. An internal thread refers to a nut or tapped hole.

Choose a value for the factor of safety.
Select the appropriate thread designation from the dropdown menu or leave it as User Defined and enter values for the basic diameter and pitch.
Select the material of the external thread from the dropdown menu or leave the material designation as User Defined and enter a value for the minimum ultimate tensile stress of the external thread material. The tensile stress value is found under external thread properties.
Choose the three values that define the tolerance grade of the external thread. These variables are automatically populated, but their values can be changed by selecting the appropriate value from their respective dropdown menus.
Select the material of the internal thread or leave the material designation as User Defined and enter a value for the minimum ultimate tensile stress for the internal thread material. The tensile stress value is found under internal thread properties.
Choose the three values that define the tolerance grade of the internal thread. These variables are automatically populated as well, but they can also be changed by selecting the appropriate value from their respective dropdown menus.
Select the calculate button to complete the analysis.
Print a report for your project recordkeeping by pressing the print button.

Assumptions

Materials are homogeneous.
The surfaces of the thread profiles are within the tolerance limits

Equations

Height of the Fundamental Triangle
$$H = \frac{\sqrt{3}}{2}p$$
Truncated Thread Height
$$h_2 = \frac{5}{8}H$$
Basic Minor Diameters
$$d_1 = D_1 = d-2\cdot h_2$$
Basic Pitch Diameter
$$d_2 = D_2 = d-\frac{3}{4}H = d-\frac{3}{8}\sqrt{3}\cdot p$$
Internal Thread Clearance Diameter
$$d_3 = d+\frac{H}{4}$$
Pitch Diameter Width
$$w_2 = \frac{p}{2}$$
Tolerance for Major Diameter External Thread
$$T_d\left(4\right) = 0.63T_d\left(6\right) \: for \: G_d = 4$$

$$T_d\left(6\right) = 180\sqrt[3]{p^2}-\frac{3.15}{\sqrt{p}} \: for \: G_d = 6$$

$$T_d\left(8\right) = 1.6T_d\left(6\right) \: for \: G_d = 8$$
Tolerance for Pitch Diameter External Thread
$$T_{d_2}\left(3\right) = 0.5T_{d_2}\left(6\right) \: for \: G_p = 3$$

$$T_{d_2}\left(4\right) = 0.63T_{d_2}\left(6\right) \: for \: G_p = 4$$

$$T_{d_2}\left(5\right) = 0.8T_{d_2}\left(6\right) \: for \: G_p = 5$$

$$T_{d_2}\left(6\right) = 90p^{0.4}d^{0.1} \: for \: G_p = 6$$

$$T_{d_2}\left(7\right) = 1.25T_{d_2}\left(6\right) \: for \: G_p = 7$$

$$T_{d_2}\left(8\right) = 1.6T_{d_2}\left(6\right) \: for \: G_p = 8$$

$$T_{d_2}\left(9\right) = 2T_{d_2}\left(6\right) \: for \: G_p = 9$$
Fundamental Deviaion of the External Thread
$$es = -\left(50+11p\right) \: for \: T_{pos} = e$$

$$es = -\left(30+11p\right) \: for \: T_{pos} = f$$

$$es = -\left(15+11p\right) \: for \: T_{pos} = g$$

$$es = 0 \: for \: T_{pos} = h$$
Adjustment Variable y
$$y = \frac{p}{8}\left\{1-\cos\left[\frac{\pi}{3}-cos^{-1}\left(1-\frac{2T_{d_2}}{p}\right)\right]\right\}$$
Adjustment Variable z
$$z = \frac{H}{4}+\frac{T_{d_2}}{2}-\frac{p}{8}$$
Minimum Major Diameter of the External Thread
$$d_{min} = d+es-T_d$$
Minimum Pitch Diameter of the External Thread
$$d_{2_{min}} = d_2+es-T_{d_2}$$
Base Width of the External Thread
$$w_E = w_2+\left(d_{2_{min}}-D_{1_{max}}\right)\tan 30$$
Circumference Per Revolution of the External Thread at D_{2_max}
$$c_E = \pi \cdot D_{1_{max}}$$
Arc Length Per Revolution of the External Thread at D_{2_max}
$$s_E = \sqrt{\left(\pi D_{1_{max}}\right)^2+p^2}$$
Tensile Stress Area
$$A_t = \frac{\pi}{4}\left(\frac{d_1+d_2+\frac{H}{6}}{2}\right)^2$$
Thread Shear Area of the External Thread Based on c_E
$$A_{s,c} = w_E \cdot c_E$$
Thread Shear Area of the External Thread Based on s_E
$$A_{s,s} = w_E \cdot s_E$$
Tolerance for Minor Diameter Internal Thread
$$T_{D_1}\left(4\right) = 0.63T_{D_1}\left(6\right) \:\: for \: G_D = 4$$

$$T_{D_1}\left(5\right) = 0.8T_{D_1}\left(6\right) \:\: for \: G_D = 5$$

$$T_{D_1}\left(6\right) = 433p-190p^{1.22} \:\: for \: p \le 0.8 \: \& \: G_D = 6$$

$$T_{D_1}\left(6\right) = 230p^{0.7} \:\: for \: p \ge 1 \: \& \: G_D = 6$$

$$T_{D_1}\left(7\right) = 1.25T_{D_1}\left(6\right) \:\: for \: G_D = 7$$

$$T_{D_1}\left(8\right) = 1.6T_{D_1}\left(6\right) \:\: for \: G_D = 8$$
Tolerance for Pitch Diameter Internal Thread
$$T_{D_2}\left(4\right) = 0.85\left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 4$$

$$T_{D_2}\left(5\right) = 1.06\left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 5$$

$$T_{D_2}\left(6\right) = 1.32\left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 6$$

$$T_{D_2}\left(7\right) = 1.7 \left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 7$$

$$T_{D_2}\left(8\right) = 2.12\left(90p^{0.4}d^{0.1}\right) \:\: for \: G_P = 8$$
Fundamental Deviation of the Internal Thread
$$EI = 15+11p \:\: for \: T_{POS} = G$$

$$EI = 0 \:\: for \: T_{POS} = H$$
Maximum Minor Diameter of the Internal Thread
$$D_{1_{max}} = D_1 + EI + T_{D_1}$$
Maximum Pitch Diameter of the Internal Thread
$$D_{2_{max}} = D_2 + EI + T_{D_2}$$
Base Width of the Internal Thread
$$w_I = w_2+\left(d_{min}-D_{2_{max}}\right)\tan 30$$
Circumference Per Revolution of the Internal Thread at D_min
$$c_I = \pi \cdot d_{min}$$
Arc Length Per Revolution of the Internal Thread at D_min
$$s_I = \sqrt{\left(\pi d_{min}\right)^2+p^2}$$
Thread Shear Area of the Internal Thread Based on c_I
$$A_{n,c} = w_I \cdot c_I$$
Thread Shear Area of the Internal Thread Based on s_I
$$A_{n,s} = w_I \cdot s_I$$
Maximum Allowable Axial Force
$$F_{max} = A_t \cdot \sigma _{t_E}$$
Minimum Required Number of External Threads
$$N_E = \frac{A_t}{A_{s,c}}$$
Minimum Required Number of Internal Threads
$$N_I = \left(\frac{\sigma _{t_E}}{\sigma _{t_I}}\right)\left(\frac{A_t}{A_{n,c}}\right)$$
Minimum Required Number of Threads Engaged
$$N_{min} = max\left(N_E,N_I\right)$$
Minimum Required Engagement Length
$$L_{e_{min}} = N_{min} \cdot p$$
Recommended Minimum Number of Threads Engaged Based On FS
$$N = FS \cdot N_{min}$$
Recommended Minimum Engagement Length Based On FS
$$L_e = N \cdot p$$

Background

a construction sign stating this section is under development