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Hand Calculations

How to review step-by-step calculation of reactions, bending moment, and shear force diagrams

SkyCiv Beam provides full hand-calculations for reactions, shear force diagrams (SFD), and bending moment diagrams (BMD). This provides a useful way to validate the results for yourself. We’re confident that you’ll find this feature useful whether you’re a student learning about the principles of structural engineering, or a professional needing to double-check the figures. To get a glimpse of our beam software, try our Free Beam Reaction Calculator which also allows you to calculate bending moment and shear force diagrams.

Hand calculations now support indeterminate beams via the moment distribution method!

Please note models with hinges and spring supports are not currently supported. For load combinations, you can access hand calculations for each combination you define in the model excluding envelope results.

FBD and Reactions

All the hand calculations can be found in the ‘Hand Calculation Wizard’ pop-up. Open this popup by clicking any of the ‘Open Hand Calculations’ buttons found under the FBD, SFD, and BMD results.

Statically Determinate Hand Calculations

The FBD and reaction results are found right at the top. The method considers static equilibrium equations.

Statically Indeterminate Hand Calculations

For indeterminate beams without hinges, the vertical and moment reactions are solved using the moment distribution method. Invented by Hardy Cross, this method is extremely powerful in it’s simplicity and has been used extensively since it was first published by the ASCE journal in 1930.

Shear Force Diagram (SFD)

The ‘Method of Sections’ or ‘Method of Cuts’ is used to determine the shear force values at locations along the beam.

Bending Moment Diagram (BMD)

Similar to the SFD results, the ‘Method of Sections’ or ‘Method of Cuts’ is used to determine the bending moment values at locations along the beam.

Hand Calculation results are also available in SkyCiv Truss and SkyCiv Section Builder software.