Simply supported reaction: RA = wL + P - RB, RB = [wL(L/2) + Pa] / L.
Simply supported shear: Vx = RA - wx - P when x is at or beyond a.
Simply supported moment: Mx = RAx - wx² / 2 - P(x - a) when x is at or beyond a.
Cantilever reaction: RA = wL + P, fixed moment = -[wL² / 2 + Pa].
Elastic deflection: service load deflection is calculated with common Euler-Bernoulli beam equations using E and I.
Factored demand: wu = factorD × wD + factorL × wL, Pu = factorD × PD + factorL × PL.
How to Use This Calculator
Choose the support condition first. Enter the beam span, evaluation point, elastic modulus, and second moment of area.
Add dead and live uniform loads. Add point loads and their position from the left support or fixed end.
Set load factors for strength summaries. Set a deflection ratio for serviceability checking.
Press Calculate. The result appears above the form and below the header section. Use the export buttons to save results.
Beam Action in Construction
Beams carry floor, roof, wall, and equipment loads across open spaces. A practical check starts with support type, span, stiffness, and the applied service loads. This calculator links those items to shear, bending moment, slope, and vertical deflection. It is useful during early sizing, site review, and comparison of member alternatives.
Why Shear and Moment Matter
Shear shows the vertical force that must pass through each section. Bending moment shows the turning demand caused by loads and reactions. High shear often controls web capacity near supports. High moment often controls flange stress near midspan or near a fixed end. Viewing both values at a chosen point helps designers understand the whole response.
Understanding Slope and Deflection
Slope is the rotation of the elastic curve. Deflection is the vertical movement of the beam. Both depend on load, span, elastic modulus, and second moment of area. A small change in span can create a large change in movement. That is why serviceability checks are important for finishes, partitions, cladding, and user comfort.
Service and Factored Loads
The tool separates service load behavior from factored strength demand. Service loads are used for slope and deflection. Factored loads are used for maximum shear and moment summaries. This helps keep movement checks and strength checks clear. The factors can be edited to match a project basis.
Using the Results Carefully
The output is an elastic estimate for common beam cases. It assumes prismatic members, small deflection behavior, and full length uniform loading. The point load is measured from the left support or fixed end. Real projects may need code checks, load combinations, lateral restraint review, connection design, vibration checks, and professional judgment.
Better Early Decisions
Early beam studies rarely need final detailing, but they do need consistent assumptions. Enter realistic stiffness values and loads from the same design stage. Review the deflection ratio before selecting a member. Compare several spans and point load positions. Keep notes on material grade, restraint, and construction tolerance. When results are close to a limit, choose a deeper section or seek a complete structural design review before drawings are issued. Clear inputs make reviews faster when teams revisit assumptions during estimating, procurement, and field coordination meetings.
FAQs
What beam types does this calculator handle?
It handles simply supported beams and cantilever beams fixed at the left end. It combines full-span uniform loads with one point load position for practical early checks.
What units should I enter?
Enter span and load positions in meters. Enter uniform loads in kN/m, point loads in kN, elastic modulus in GPa, and inertia in cm^4.
Are slope and deflection service values?
Yes. The calculator uses service loads for slope and deflection. This matches common serviceability review practice, where movement is checked under unfactored load effects.
Why are factored results included?
Factored shear and moment help compare strength demand. You can edit dead and live load factors to suit your project basis or office standard.
Can this replace structural design?
No. It is an estimating and checking tool. Final construction documents should include code checks, member capacity, stability, connections, load paths, and professional review.
Why does inertia strongly affect deflection?
Deflection is inversely related to EI. A larger second moment of area increases stiffness and reduces movement under the same load and span.
Where is the point load measured from?
The point load position is measured from the left support for a simply supported beam. It is measured from the fixed end for a cantilever.
What does a failed deflection check mean?
It means the maximum estimated deflection exceeds your selected limit. Consider a deeper member, shorter span, lower load, added support, or refined structural analysis.