Calculations

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Calculations

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Maximum deflection

Maximum deflection in beam with fixed support on both ends due to two forces equally spaced from the middle.

$$ \Delta_{max_{2pfs}} = {{\left({ P \cdot l ^ 3 }\right) \over \left({ 6 \cdot E \cdot I }\right)} \cdot \left({ {3 \over 4} \cdot \left({ {a \over l} }\right) ^ 2 - \left({ {a \over l} }\right) ^ 3 }\right)} \; \; , {mm} $$

Custom section moment of inertia

Calculate moment of inertia for custom section.

Moment of inertia

$$ I_{xx_{custom}} = {{\left({ B \cdot H ^ 3 - b \cdot h ^ 3 }\right) \over 12}} \; \; , {mm ^ 4} $$

Maximum bending deflection

Maximum deflection of simply supported beam subject to two equal loads at equal distance from supports.

Maximum deflection

$$ \Delta_{max_{2P_{1}}} = {{\left({ P \cdot a }\right) \over \left({ 24 \cdot E \cdot I }\right)} \cdot \left({ 3 \cdot l ^ 2 - 4 \cdot a ^ 2 }\right)} \; \; , {mm} $$

Cylinder volume

Volume of solid cylinder

$$ V_{cylinder} = {\pi \cdot h \cdot {D ^ 2 \over 4}} \; \; , {m ^ 3} $$

Cylinder mass

Mass of solid cylinder

Solid cylinder mass

$$ m_{cylinder} = {V_{cylinder} \cdot \rho} \; \; , {kg} $$

Mass

Calculate mass for given volume and density.

Mass

$$ m_{custom} = {V \cdot \rho} \; \; , {kg} $$

Energy

Calculate energy based on mass and velocity.

$$ W_{mV} = {{\left({ m \cdot V ^ 2 }\right) \over 2}} \; \; , {J} $$

Crane classification

Group classification for the crane as a whole

Crane classification

$$ Crane class = A8 \; \; $$

Gravity of Earth

Standard Earth gravity

$$ g = {9.80665} \; \; , {{m \over s ^ 2}} $$

Capacity factor

Capacity factor for strength limit states as per AS 4100:2020 Table 3.4

$$ \phi_{ls_{AS4100}} = {0.6} \; \; $$

Linear speed to rpm

Convert linear speed in m/min to rotating speed in rpm.

Linear speed

$$ n_{travel} = {{v \over \left({ \pi \cdot D }\right)}} \; \; , {rpm} $$

Output torque Tq - without inertia

Calculate output torque to be used in minimum shaft diameter calculation as per AS1403:2004 Table 1, for "Inertia not significant" option.

Output torque

$$ T_q = {T_M \cdot {N_1 \over N_2} \cdot \eta_{1\over2}} \; \; $$

Linear interpolation

Find Y coordinate for a specified X coordinate on a linear function determined by two points.

Y coordinate

$$ Y_{LI} = {y_1 + {\left({ y_2 - y_1 }\right) \over \left({ x_2 - x_1 }\right)} \cdot \left({ X - x_1 }\right)} \; \; $$

Combined shear force per bolt in a bolt group

Calculates required shear or slip resistance of the critical bearing or friction grip bolt in bolt group. SABS0162.

$$ F_{R_{bg}} = {\sqrt{ F_{3_{bg}} ^ 2 + \left({ F_{1_{bg}} + F_{2_{bg}} }\right) ^ 2 }} \; \; , {kN} $$

Combined tension and shear in bearing connection

Check combined shear and tension in bearing type bolted connection. SABS0162.

Combined tension and shear ratio

$$ r_{tsc} = {{T_{1_{bg}} \over T_r} + {F_{R_{bg}} \over V_r}} \; \; $$

Bolt group polar moment of inertia

Polar moment of inertia

$$ I_{bg} = {\left({ n_{c_{bg}} \cdot {n_{r_{bg}} \over 12} }\right) \cdot \left({ s_{r_{bg}} ^ 2 \cdot \left({ n_{r_{bg}} ^ 2 - 1 }\right) + s_{c_{bg}} ^ 2 \cdot \left({ n_{c_{bg}} ^ 2 - 1 }\right) }\right)} \; \; , {mm ^ 2} $$

Bolt group load

$$ P_{bg} = {90} \; \; , {kN} $$

Bolt force without eccentricity

Vertical bolt force without eccentricity

$$ F_{1_{bg}} = {{P_{bg} \over \left({ n_{c_{bg}} \cdot n_{r_{bg}} }\right)}} \; \; , {kN} $$

Bolt group shear load eccentricity

Eccentricity of load causing shear stress from bolt group centroid.

Shear load eccentricity

$$ e_{s_{bg}} = {275} \; \; , {mm} $$

Bolt group row spacing

$$ s_{r_{bg}} = {70} \; \; , {mm} $$

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