Calculations

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Calculations

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Reference buckling moment

Reference buckling moment as per AS 4100:2020 Section 5.6.1.1

Reference buckling moment

$$ M_{o_{AS4100}} = {{\sqrt{ \pi ^ 2 \cdot E \cdot {I_{y_{AS4100}} \over l_{e_{AS4100}} ^ 2} \cdot \left({ G \cdot J_{RHS} + \pi ^ 2 \cdot E \cdot {I_{w_{AS4100}} \over l_{e_{AS4100}} ^ 2} }\right) } \over 10 ^ 3}} \; \; , {Nmm} $$

Moment modification factor

Moment modification factor as per AS4100:2020 Section 5.6.1.1

$ \alpha_{m_{cal_{AS4100}}} $ < $ 1 $

$$ \alpha_{m_{AS4100}} = {\alpha_{m_{cal_{AS4100}}}} $$

$$ \alpha_{m_{AS4100}} = {1} $$

Elastic section moduli

Elastic section moduli

$$ Z_{x_{AS4100}} = {430000} \; \; , {mm ^ 3} $$

Nominal member moment capacity

The nominal member moment capacity as per AS4100:2020 Section 5.6.1.1(1)

Nominal member moment capacity

$$ M_{b_{AS4100}} = {\alpha_{m_{AS4100}} \cdot \alpha_{s_{AS4100}} \cdot M_{s_{AS4100}}} \; \; , {Nm} $$

Shear stress

Calculate shear stress in a custom rectangular solid section under point load.

Shear stress

$$ \tau_{shear_{rectangle}} = {{F_N \over \left({ A_{rectangle} \cdot n_{sp} }\right)}} \; \; , {MPa} $$

Bending stress

Calculate normal stress in a custom rectangular solid section due to bending moment.

Bending stress

$$ \sigma_{bend_{SQ}} = {10 ^ 3 \cdot {M_{B_p} \over W_{y_{rectangle}}}} \; \; , {MPa} $$

Distance

$$ a_{\Delta} = {100} \; \; , {mm} $$

Distance

$$ b_{\Delta} = {100} \; \; , {mm} $$

Compression stress

Calculate compression stress in a custom rectangular solid section under point load.

Compression stress

$$ \sigma_{comp_{1P}} = {{F_N \over A_{rectangle}}} \; \; , {MPa} $$

Area of rectangular hollow section

Area of rectangular hollow section

Area

$$ A_{rectangle} = {H \cdot B} \; \; , {mm ^ 2} $$

Area of belt conveyor

Area required for a belt conveyor with known mass flow rate and bulk material density.

Required area

$$ A_{conv_{mass}} = {{( Q \cdot 10 ^ 6 ) \over \left({ v_{conv} \cdot 3600 \cdot \rho_{bm} }\right)}} \; \; , {mm ^ 2} $$

Belt conveyor capacity

Theoretical mass flow rate of a belt conveyor with known area and material density.

Mass flow rate

$$ Q_{conv_m} = {{A \over 10 ^ 6} \cdot v_{conv} \cdot 3600 \cdot \rho_{bm}} \; \; , {{kg \over h}} $$

Conveyor speed

Conveying speed

Conveyor speed

$$ v_{conv} = {2} \; \; , {{m \over s}} $$

Base of triangle

Calculates base of isosceles triangle for given area and base angle.

Base length

$$ c_{isos} = {\sqrt{ {( 2 \cdot A ) \over \tan( \alpha_{rad} )} }} \; \; , {mm} $$

Area of triangle

Calculates area of isosceles triangle by given base and base angle

Area

$$ A_{isos_{\alpha}} = {{c ^ 2 \over 2} \cdot \tan( \alpha_{rad} )} \; \; , {mm ^ 2} $$

Angle

Convert angle from degrees to radians

Angle in radians

$$ \alpha_{rad} = {\alpha_{deg} \cdot {\pi \over 180}} \; \; , {rad} $$

Electrical motor power

Electrical motor power from nominal torque and rotational speed.

Motor power

$$ P_n = {{( T_n \cdot n_n ) \over 9550}} \; \; , {kW} $$

Gearbox reduction ratio

Reduction ratio of 4 stage gearbox

Four stage gearbox ratio

$$ i_{gb4} = {i_{gr1} \cdot i_{gr2} \cdot i_{gr3} \cdot i_{gr4}} \; \; $$

Gear reduction ratio

Reduction ratio of two gear wheels using number of teeth

Fourth stage ratio

$$ i_{gr4} = {z_8 \over z_7} \; \; $$

Gear reduction ratio

Reduction ratio of two gear wheels using number of teeth

Third stage ratio

$$ i_{gr3} = {z_6 \over z_5} \; \; $$