Calculations

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Calculations

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Beam length

$$ l_{\Delta} = {a_{\Delta} + b_{\Delta}} \; \; , {mm} $$

Maximum bending deflection

Maximum deflection of simply supported beam subject to distributed load applied over its full length.

Maximum deflection

$$ \Delta_{max_{dis_{full}}} = {{\left({ 5 \cdot W \cdot l_{\Delta} ^ 3 }\right) \over \left({ 384 \cdot E \cdot I }\right)}} \; \; , {mm} $$

Force from torque

Calculate force resulting from torque at specific distance.

$$ F_{torque} = {{T \over a}} \; \; , {N} $$

Minimum shaft diameter - AS1403 F3

Minimum shaft diameter as per AS1403 Table 2 Formula 3 for power applied and torque reversal conditions.

Minimum shaft diameter

$$ D_{min_{AS1403_{F3}}} = {\left({ 10 ^ 4 \cdot {F_S \over F_R} \cdot K_S \cdot K \cdot \sqrt{ \left({ M_q + {\left({ P_q \cdot D_{try} }\right) \over 8000} }\right) ^ 2 + {3 \over 4} \cdot T_q ^ 2 } }\right) ^ \left({ {1 \over 3} }\right)} \; \; , {mm} $$

Minimum shaft diameter - AS1403 F1

Minimum shaft diameter as per AS1403 Table 2 Formula 1

Minimum shaft diameter

$$ D_{min_{AS1403_{F1}}} = {\left({ 10 ^ 4 \cdot {F_S \over F_Y} \cdot \sqrt{ \left({ M_q + {\left({ P_q \cdot D_{try} }\right) \over 8000} }\right) ^ 2 + {3 \over 4} \cdot T_q ^ 2 } }\right) ^ \left({ {1 \over 3} }\right)} \; \; , {mm} $$

Second moment of area

Second moment of area for solid circular section

Second moment

$$ I_{circular_{solid}} = {{\left({ \pi \cdot D ^ 4 }\right) \over 64}} \; \; , {mm ^ 4} $$

Bending moment

Maximum bending moment in simply supported beam under uniform load over its full length.

$$ M_{B_{d_{max_{full}}}} = {{\left({ W_d \cdot l }\right) \over 8}} \; \; , {Nm} $$

Bending stress

Calculate normal stress in a section, with known section modulus, due to bending caused by distributed load over its full length

Bending stress

$$ \sigma_{bend_{d_{max_{full}}}} = {10 ^ 3 \cdot {M_{B_{d_{max_{full}}}} \over W_{y_{section}}}} \; \; , {MPa} $$

CHS inside diameter

Calculate inside diameter of circular hollow section for given section modulus and outside diameter

Inside diameter

$$ d_{CHS_{req}} = {\left({ D ^ 4 - \left({ {32 \over \pi} \cdot W \cdot D }\right) }\right) ^ \left({ {1 \over 4} }\right)} \; \; , {mm} $$

Maximum bending deflection

Maximum deflection of simply supported beam subject to single point load applied off centre.

Maximum deflection

$$ \Delta_{max_{1P}} = {{\left({ P \cdot a_{\Delta} \cdot b_{\Delta} \cdot \left({ a_{\Delta} + 2 \cdot b_{\Delta} }\right) \cdot \sqrt{ 3 \cdot a_{\Delta} \cdot \left({ a_{\Delta} + 2 \cdot b_{\Delta} }\right) } }\right) \over \left({ 27 \cdot E \cdot I \cdot l_{\Delta} }\right)}} \; \; , {mm} $$

Section modulus of CHS

Section modulus of circular hollow section with known diameters

Section modulus

$$ W_{y_{CHS}} = {{\pi \over 32} \cdot \left({ {\left({ D ^ 4 - d ^ 4 }\right) \over D} }\right)} \; \; , {mm ^ 3} $$

Bin discharge time (h)

Time, in hours (h), required to discharge bin with given volumetric capacity and volumetric flow rate.

Discharge time

$$ t_{bin_{discharge}} = {{V_{bin} \over Q_{vol}}} \; \; , {h} $$

Bin discharge time (min)

Time, in minutes (min), required to discharge bin with given volumetric capacity and volumetric flow rate.

Discharge time

$$ t_{bin_{discharge_{min}}} = {\left({ {V_{bin} \over Q_{vol}} }\right) \cdot 60} \; \; , {min} $$

Volumetric flow rate

Convert mass flow rate to volumetric flow rate.

Volumetric flow rate

$$ Q_{vol} = {{Q_{mass} \over \rho_{prod}}} \; \; , {{m ^ 3 \over h}} $$

Gearbox reduction ratio

Reduction ratio of 2 stage gearbox

Two stage gearbox ratio

$$ i_{gb2} = {i_{gr1} \cdot i_{gr2}} \; \; $$

Section modulus of RHS

Section modulus of square hollow section (RHS)

Section modulus

$$ W_{y_{RHS}} = {{\left({ B \cdot H ^ 3 - b \cdot h ^ 3 }\right) \over \left({ 6 \cdot H }\right)}} \; \; , {mm ^ 3} $$

Triangular prism volume

Volume of triangular prism.

$$ V_{prism_{tri}} = {\left({ {\left({ w_{base} \cdot h_{base} }\right) \over 2} }\right) \cdot h_{prism}} \; \; , {m ^ 3} $$

Combined volume

Combined volume of rectangular prism and triangular prism.

Combined volume

$$ V_{comb_{rec-tri}} = {V_{prism_{rec}} + V_{prism_{tri}}} \; \; , {m ^ 3} $$

Rectangular prism volume

Volume of rectangular prism.

$$ V_{prism_{rec}} = {w_{base} \cdot l_{base} \cdot h} \; \; , {m ^ 3} $$

Design bending moment in RHS

Design bending moment in RHS about the major principal axis analyzed by the elastic methos as per AS4100:2020 Section 4.4.2.2

$$ M_{x_{AS4100}} = {\phi_{ls_{AS4100}} \cdot M_{b_{AS4100}}} \; \; , {Nm} $$