Example engineering calculations

Beam Deflection Check

Calculating the deflection of a simply supported beam

Simply Supported Beam Deflection (UDL)

Maximum mid-span deflection and bending stress of a simply supported beam under a uniformly distributed load.

Simply Supported Beam UDL

Simply Supported Beam under uniform distributed load

Slender Column Buckling

Cantilever Beam Deflection (End Point Load)

Tip deflection and root bending stress of a cantilever beam loaded by a point force at its free end.

Euler Buckling Load of a Column

Critical elastic buckling load and stress of a slender column from the Euler formula.

Simply Supported Beam Reactions (Point Load)

Support reactions of a simply supported beam carrying a single point load at an arbitrary position.

Maximum Bending Moment (Simply Supported UDL)

Peak mid-span bending moment of a simply supported beam under a uniformly distributed load.

Section Modulus and Bending Stress

Elastic section modulus of a rectangular section and the bending stress it produces under a given moment.

Plastic Moment Capacity (Rectangular)

Plastic section modulus and fully-plastic moment of a rectangular section.

Column Slenderness Ratio

Radius of gyration and slenderness ratio of a column, the key parameter for buckling.

Combined Axial and Bending Stress

Peak fibre stress in a member carrying simultaneous axial load and bending moment.

Fillet Weld Shear Strength

Throat area and shear stress of a fillet weld carrying a direct load.

Maximum Shear Stress in a Rectangular Beam

Peak transverse shear stress at the neutral axis of a rectangular beam section.

Fixed-Fixed Beam Deflection (UDL)

Mid-span deflection of a built-in (fixed-fixed) beam under a uniformly distributed load.

Cantilever Deflection Under a UDL

Tip deflection of a cantilever beam carrying a uniformly distributed load along its length.

Fixed-End Moment (UDL)

Fixed-end moment of a built-in beam under a uniformly distributed load.

Mid-Span Deflection (Central Point Load)

Mid-span deflection of a simply supported beam under a central point load.

Radius of Gyration of a Section

Radius of gyration of a cross-section from its second moment of area and area.

Web Shear Stress in a Beam

Average shear stress in the web of a beam from the shear force and web dimensions.

Bearing Stress at a Bolt Hole

Bearing stress of a bolt against the plate it presses on.

Bolt Tensile Stress

Tensile stress in a bolt from the applied tension and its stress area.

Allowable Stress (ASD)

Allowable working stress from the yield strength and a factor of safety.

Truss Diagonal Member Force

Axial force in a truss diagonal carrying a panel shear.