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Second moment of area - rectangle
public
Second moment of area for solid rectangular section
Second moment
$$ I_{rectangular_{solid}} = {{\left({ b \cdot h ^ 3 }\right) \over 12}} \; \; , {mm ^ 4} $$
Second moment of area - SQ
public
Second moment of area for square solid section
Second moment
$$ I_{square_{solid}} = {{a ^ 4 \over 12}} \; \; , {mm ^ 4} $$
Second moment of area - CHS
public
Second moment of area for circular hollow section
Second moment
$$ I_{circular_{hollow}} = {\left({ D ^ 4 - d ^ 4 }\right) \cdot {\pi \over 64}} \; \; , {mm ^ 4} $$
Second moment of area - round
public
Second moment of area for solid circular section
Second moment
$$ I_{circular_{solid}} = {{\left({ \pi \cdot D ^ 4 }\right) \over 64}} \; \; , {mm ^ 4} $$
Torsion modulus of circular section
public
Torsion modulus of circular solid section with known diameter
Torsion modulus
$$ W_{t_{circle}} = {{\left({ \pi \cdot D_{circle_{mm}} ^ 3 }\right) \over 16}} \; \; , {mm ^ 3} $$
Bending stress
public
Calculate normal stress in simply supported beam due to bending caused by single force.
Bending stress
$$ \sigma_{bend_{p_{max}}} = {10 ^ 3 \cdot {M_{B_{p_{max}}} \over W_{y_{section}}}} \; \; , {MPa} $$
Section modulus of circular section
public
Section modulus of circular solid section with known diameter
Section modulus
$$ W_{y_{circle}} = {{\left({ \pi \cdot D_{circle_{mm}} ^ 3 }\right) \over 32}} \; \; , {mm ^ 3} $$
Section modulus of rectangular section
public
Section modulus of rectangular solid section.
Section modulus
$$ W_{y_{rectangle}} = {{\left({ b \cdot h ^ 2 }\right) \over 6}} \; \; , {mm ^ 3} $$
Section modulus of square section
public
Section modulus of square solid section.
Section modulus
$$ W_{y_{square}} = {{a ^ 3 \over 6}} \; \; , {mm ^ 3} $$
Section modulus of RHS
public
Section modulus of square hollow section (RHS)
Section modulus
$$ W_{y_{RHS}} = {{\left({ B \cdot H ^ 3 - b \cdot h ^ 3 }\right) \over \left({ 6 \cdot H }\right)}} \; \; , {mm ^ 3} $$
CHS inside diameter
public
Calculate inside diameter of circular hollow section for given section modulus and outside diameter
Inside diameter
$$ d_{CHS_{req}} = {\left({ D ^ 4 - \left({ {32 \over \pi} \cdot W \cdot D }\right) }\right) ^ \left({ {1 \over 4} }\right)} \; \; , {mm} $$
Torsion modulus of CHS
public
Torsion modulus of circular hollow section with known diameters
Section modulus
$$ W_{t_{CHS}} = {{\pi \over 16} \cdot \left({ {\left({ D ^ 4 - d ^ 4 }\right) \over D} }\right)} \; \; , {mm ^ 3} $$
Section modulus of CHS
public
Section modulus of circular hollow section with known diameters
Section modulus
$$ W_{y_{CHS}} = {{\pi \over 32} \cdot \left({ {\left({ D ^ 4 - d ^ 4 }\right) \over D} }\right)} \; \; , {mm ^ 3} $$
Bending stress
public
Calculate normal stress in simply supported beam, with known section modulus, due to bending caused by 2 symmetrical point loads.
Bending stress
$$ \sigma_{bend_{2p}} = {10 ^ 3 \cdot {M_{B_2p} \over W_{y_{section}}}} \; \; , {MPa} $$
Moment modification factor
public
Moment modification factor for segments fully or partially restrained at both ends
Moment modification factor calculated
$$ \alpha_{m_{cal_{AS4100}}} = {1.0 + 0.35 \cdot \left({ 1 - {\left({ 2 \cdot a }\right) \over l} }\right) ^ 2} \; \; $$
Design bending moment in RHS
public
Design bending moment in RHS about the major principal axis analyzed by the elastic method as per AS4100:2020 Section 4.4.2.2
$$ M_{x_{AS4100}} = {\phi_{ls_{AS4100}} \cdot M_{b_{AS4100}}} \; \; , {Nm} $$
Gear wheel radial force
public
Radial force as a result of peripheral force in a gear wheel.
Radial force
$$ P_r = {P_h \cdot \tan\left({ \alpha_n \cdot {\pi \over 180} }\right)} \; \; , {N} $$
Combined bending in 2 planes
public
Combined bending
$$ M_{B_{comb}} = {\sqrt{ M_{B_1} ^ 2 + M_{B_2} ^ 2 }} \; \; , {Nm} $$
Gearbox output speed
public
Output speed
$$ n_2 = {{n_1 \over i}} \; \; , {rpm} $$
Shear stress
public
Calculate shear stress in a shaft due to torsion.
Shear stress
$$ \tau_{shear_{shaft}} = {{\left({ T_N \cdot 10 ^ 3 }\right) \over W_{t_{circle}}}} \; \; , {MPa} $$
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