This page provides a set of interactive plots for common stress concentration factors. See the reference section for more details.
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).
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:
$$ \sigma_{nom} = { F \over (w - d)t } $$Input Geometry:
Results:
d/w:
K_{t}:
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:
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.
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:
$$ \sigma_{nom} = { M \over S } = { 6M \over (w - d) t^2 } $$Input Geometry:
Results:
d/t:
d/w:
K_{t}:
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:
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).
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:
$$ \sigma_{nom} = { F \over (w - 2h)t } = { F \over dt } $$Input Geometry:
Results:
d:
w/d:
r/d:
h/r:
K_{t}:
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:
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.
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:
$$ \sigma_{nom} = { 6M \over t (w - 2h)^2 } = { 6M \over t d^2 } $$Input Geometry:
Results:
d:
w/d:
r/d:
h/r:
K_{t}:
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:
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).
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:
$$ \sigma_{nom} = { F \over dt } $$Input Geometry:
Results:
h:
r/d:
D/d:
h/r:
K_{t}:
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:
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.
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:
$$ \sigma_{nom} = { 6M \over t d^2 } $$Input Geometry:
Results:
h:
r/d:
D/d:
h/r:
K_{t}:
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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