This page provides a set of interactive plots for common stress concentration factors. See the reference section for more details.

### Rectangular Bar With Central Hole, Axial Force

This tab defines the stress concentration factor for a bar with a rectangular cross section and a central circular hole. The bar has an applied axial force (tensile or compressive).

• w = bar width
• d = hole diameter
• t = bar thickness
• F = applied force (tensile or compressive)
Cannot display plot -- browser is out of date.

The maximum stress is calculated as $$\sigma_{max} = K_t \cdot \sigma_{nom}$$, where $$K_t$$ is the stress concentration factor as determined from the plot below, and $$\sigma_{nom}$$ is calculated as:

$$\sigma_{nom} = { F \over (w - d)t }$$
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Input Geometry:

Results:

d/w:

Kt:

The value of the stress concentration factor is calculated by:

$$K_t = 3 - 3.13 \left({ d \over w }\right) + 3.66 \left({ d \over w }\right)^2 - 1.53 \left({ d \over w }\right)^3$$

Sources:

### Rectangular Bar With Central Hole, Out-of-Plane Bending

This tab defines the stress concentration factor for a bar with a rectangular cross section and a central circular hole. The bar has an applied out-of-plane bending moment.

• w = bar width
• d = hole diameter
• t = bar thickness
• M = applied bending moment
Cannot display plot -- browser is out of date.

The maximum stress is calculated as $$\sigma_{max} = K_t \cdot \sigma_{nom}$$, where $$K_t$$ is the stress concentration factor as determined from the plot below, and $$\sigma_{nom}$$ is calculated as:

$$\sigma_{nom} = { M \over S } = { 6M \over (w - d) t^2 }$$
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Input Geometry:

Results:

d/t:

d/w:

Kt:

The value of the stress concentration factor is calculated by:

$$K_t = \left[ 1.79 + { 0.25 \over 0.39 + (d/t) } + { 0.81 \over 1 + (d/t)^2 } - { 0.26 \over 1 + (d/t)^3 } \right] \left[ 1 - 1.04 \left({d \over w }\right) + 1.22 \left({d \over w }\right)^2 \right]$$

Sources:

### Rectangular Bar With U-Notches, Axial Force

This tab defines the stress concentration factor for a bar with a rectangular cross section and two U-notches. The bar has an applied axial force (tensile or compressive).

• w = bar width
• h = notch height
• t = bar thickness
• F = applied force (tensile or compressive)
Cannot display plot -- browser is out of date.

The maximum stress is calculated as $$\sigma_{max} = K_t \cdot \sigma_{nom}$$, where $$K_t$$ is the stress concentration factor as determined from the plot below, and $$\sigma_{nom}$$ is calculated as:

$$\sigma_{nom} = { F \over (w - 2h)t } = { F \over dt }$$
Cannot display plot -- browser is out of date.

Input Geometry:

Results:

d:

w/d:

r/d:

h/r:

Kt:

The value of the stress concentration factor is calculated by:

$$K_t = C_1 + C_2 \left({ 2h \over w }\right) + C_3 \left({ 2h \over w }\right)^2 + C_4 \left({ 2h \over w }\right)^3$$

where the coefficients in the equation above are calculated from "Peterson's Stress Concentration Factors":

$$0.1 \le h/r \le 2.0$$ $$2.0 \le h/r \le 50.0$$
$$C_1$$ $$0.955 + 2.169 \sqrt{h/r} - 0.081 (h/r)$$ $$1.037 + 1.991 \sqrt{h/r} + 0.002 (h/r)$$
$$C_2$$ $$-1.557 - 4.046 \sqrt{h/r} + 1.032 (h/r)$$ $$-1.886 - 2.181 \sqrt{h/r} - 0.048 (h/r)$$
$$C_3$$ $$4.013 + 0.424 \sqrt{h/r} - 0.748 (h/r)$$ $$0.649 + 1.086 \sqrt{h/r} + 0.142 (h/r)$$
$$C_4$$ $$-2.461 + 1.538 \sqrt{h/r} - 0.236 (h/r)$$ $$1.218 - 0.922 \sqrt{h/r} - 0.086 (h/r)$$

Sources:

### Rectangular Bar With U-Notches, Bending

This tab defines the stress concentration factor for a bar with a rectangular cross section and two U-notches. The bar has an applied in-plane bending moment.

• w = bar width
• h = notch height
• t = bar thickness
• M = applied bending moment
Cannot display plot -- browser is out of date.

The maximum stress is calculated as $$\sigma_{max} = K_t \cdot \sigma_{nom}$$, where $$K_t$$ is the stress concentration factor as determined from the plot below, and $$\sigma_{nom}$$ is calculated as:

$$\sigma_{nom} = { 6M \over t (w - 2h)^2 } = { 6M \over t d^2 }$$
Cannot display plot -- browser is out of date.

Input Geometry:

Results:

d:

w/d:

r/d:

h/r:

Kt:

The value of the stress concentration factor is calculated by:

$$K_t = C_1 + C_2 \left({ 2h \over w }\right) + C_3 \left({ 2h \over w }\right)^2 + C_4 \left({ 2h \over w }\right)^3$$

where the coefficients in the equation above are calculated from "Peterson's Stress Concentration Factors":

$$0.1 \le h/r \le 2.0$$ $$2.0 \le h/r \le 50.0$$
$$C_1$$ $$1.024 + 2.092 \sqrt{h/r} - 0.051 (h/r)$$ $$1.113 + 1.957 \sqrt{h/r}$$
$$C_2$$ $$-0.630 - 7.194 \sqrt{h/r} + 1.288 (h/r)$$ $$-2.579 - 4.017 \sqrt{h/r} - 0.013 (h/r)$$
$$C_3$$ $$2.117 + 8.574 \sqrt{h/r} - 2.160 (h/r)$$ $$4.100 + 3.922 \sqrt{h/r} + 0.083 (h/r)$$
$$C_4$$ $$-1.420 - 3.494 \sqrt{h/r} + 0.932 (h/r)$$ $$-1.528 - 1.893 \sqrt{h/r} - 0.066 (h/r)$$

Sources:

### Rectangular Bar With Fillet, Axial Force

This tab defines the stress concentration factor for a bar with a rectangular cross section and a fillet. The bar has an applied axial force (tensile or compressive).

• D = width of larger section
• d = width of smaller section
• r = radius of fillet
• t = bar thickness
• F = applied force (tensile or compressive)
Cannot display plot -- browser is out of date.

The maximum stress is calculated as $$\sigma_{max} = K_t \cdot \sigma_{nom}$$, where $$K_t$$ is the stress concentration factor as determined from the plot below, and $$\sigma_{nom}$$ is calculated as:

$$\sigma_{nom} = { F \over dt }$$
Cannot display plot -- browser is out of date.

Input Geometry:

Results:

h:

r/d:

D/d:

h/r:

Kt:

The value of the stress concentration factor is calculated by:

$$K_t = C_1 + C_2 \left({ 2h \over D }\right) + C_3 \left({ 2h \over D }\right)^2 + C_4 \left({ 2h \over D }\right)^3$$

where the coefficients in the equation above are calculated from "Roark's Formulas for Stress and Strain":

$$0.1 \le h/r \le 2.0$$ $$2.0 \le h/r \le 20.0$$
$$C_1$$ $$1.007 + 1.000 \sqrt{h/r} - 0.031 (h/r)$$ $$1.042 + 0.982 \sqrt{h/r} - 0.036 (h/r)$$
$$C_2$$ $$-0.114 - 0.585 \sqrt{h/r} + 0.314 (h/r)$$ $$-0.074 - 0.156 \sqrt{h/r} - 0.010 (h/r)$$
$$C_3$$ $$0.241 - 0.992 \sqrt{h/r} - 0.271 (h/r)$$ $$-3.418 + 1.220 \sqrt{h/r} - 0.005 (h/r)$$
$$C_4$$ $$-0.134 + 0.577 \sqrt{h/r} - 0.012 (h/r)$$ $$3.450 - 2.046 \sqrt{h/r} + 0.051 (h/r)$$

Sources:

### Rectangular Bar With Fillet, Bending

This tab defines the stress concentration factor for a bar with a rectangular cross section and a fillet. The bar has an applied in-plane bending moment.

• D = width of larger section
• d = width of smaller section
• r = radius of fillet
• t = bar thickness
• M = applied bending moment
Cannot display plot -- browser is out of date.

The maximum stress is calculated as $$\sigma_{max} = K_t \cdot \sigma_{nom}$$, where $$K_t$$ is the stress concentration factor as determined from the plot below, and $$\sigma_{nom}$$ is calculated as:

$$\sigma_{nom} = { 6M \over t d^2 }$$
Cannot display plot -- browser is out of date.

Input Geometry:

Results:

h:

r/d:

D/d:

h/r:

Kt:

The value of the stress concentration factor is calculated by:

$$K_t = C_1 + C_2 \left({ 2h \over D }\right) + C_3 \left({ 2h \over D }\right)^2 + C_4 \left({ 2h \over D }\right)^3$$

where the coefficients in the equation above are calculated from "Roark's Formulas for Stress and Strain":

$$0.1 \le h/r \le 2.0$$ $$2.0 \le h/r \le 20.0$$
$$C_1$$ $$1.007 + 1.000 \sqrt{h/r} - 0.031 (h/r)$$ $$1.042 + 0.982 \sqrt{h/r} - 0.036 (h/r)$$
$$C_2$$ $$-0.270 - 2.404 \sqrt{h/r} + 0.749 (h/r)$$ $$-3.599 + 1.619 \sqrt{h/r} - 0.431 (h/r)$$
$$C_3$$ $$0.677 + 1.133 \sqrt{h/r} - 0.904 (h/r)$$ $$6.084 - 5.607 \sqrt{h/r} + 1.158 (h/r)$$
$$C_4$$ $$-0.414 + 0.271 \sqrt{h/r} + 0.186 (h/r)$$ $$-2.527 + 3.006 \sqrt{h/r} - 0.691 (h/r)$$

Sources:

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