Formula Used
This calculator models a simply supported beam with a hinge support at the left end and a roller support at the right end.
Total vertical load: W = P + wL
Right reaction: RB = (P × x + wL × L / 2) / L
Left hinge reaction: RA = W - RB
Horizontal hinge reaction: HA = -A, where A is the axial end load.
Shear at distance z: V(z) = RA - wz - P, after the point load.
Moment at distance z: M(z) = RAz - wz² / 2 - P(z - x), after the point load.
Bending stress: f = M / S
Deflection is estimated from curvature, where curvature equals M / EI.
How to Use This Calculator
Select the unit system first. Enter the beam span. Add the point load and its location from the hinge. Enter the uniform load over the full span. Use the load factor for service or factored checks. Add material and section properties. Press the calculate button. Review reactions, moment, shear, stress, and deflection.
Example Data Table
| Case |
Span |
Point Load |
Load Position |
Uniform Load |
Use |
| Floor beam |
6 m |
12 kN |
3 m |
5 kN/m |
Service check |
| Roof beam |
4.8 m |
8 kN |
2.2 m |
3.5 kN/m |
Snow load check |
| Mezzanine beam |
7.5 m |
20 kN |
4 m |
6 kN/m |
Storage check |
Hinged Beam Planning Guide
A hinged beam is common in building work. It has a pin support at one end. The pin can resist vertical load. It can also resist horizontal load. It does not resist end moment. This makes the end free to rotate. The opposite support is often a roller. That support carries vertical load only.
Why hinge behavior matters
A hinge changes the bending pattern. The bending moment at the hinge is zero. Loads must travel through shear and reaction forces. This calculator helps you test that path. It estimates support reactions, peak shear, peak bending moment, bending stress, and service deflection. It is useful during early sizing. It also helps compare load cases before detailed design.
Inputs used by the calculator
Enter the span first. Then add the main point load and its distance from the hinge. Add a uniform load for self weight, finishes, storage, or live load. Use the load factor when you want a quick factored case. Enter elastic modulus and moment of inertia for deflection. Enter section modulus and allowable stress for a basic strength check.
Reading the results
The left reaction belongs to the hinge support. The right reaction belongs to the roller support. The horizontal reaction equals the entered axial load. The maximum shear shows the largest vertical force inside the member. The maximum moment helps size the section. The deflection estimate checks serviceability. The stress ratio compares calculated bending stress with the allowable value.
Construction use
Use conservative loads when exact site values are not known. Keep units consistent. Review span, load position, and member properties carefully. A small change in span can greatly change deflection. Export the report for notes, checking, or discussion. Final beam sizes should be confirmed by a qualified engineer. Local codes, connection capacity, bearing length, lateral bracing, and load combinations may control the design.
Practical checks
Check both service and factored loads. Compare dead load, live load, and equipment load when they differ. Keep the point load within the clear span. Treat crane, hoist, wall, and tank loads with extra care. For timber, steel, or concrete beams, use material properties from reliable data. Also check supports. Strong members can still fail at weak connections.
FAQs
What is a hinged beam?
A hinged beam has a pin support that permits rotation. It can resist vertical and horizontal reaction forces. It does not resist bending moment at the hinge point.
Does the hinge carry moment?
No. An ideal hinge has zero moment resistance. The calculator assumes the hinge end moment is zero, so loads are balanced through reactions and shear.
What support system is used here?
This page uses a hinge at the left end and a roller at the right end. That is a common simply supported beam model.
Can I enter factored loads?
Yes. Enter service loads and use the load factor field. A factor of 1.0 keeps loads unchanged. Higher factors create a quick design load case.
What does maximum moment mean?
Maximum moment is the largest bending demand found along the span. It is used with section modulus to estimate bending stress.
How is deflection estimated?
The calculator uses the bending moment curve and integrates curvature. Curvature is based on M divided by EI. The result is a serviceability estimate.
Why enter section modulus?
Section modulus connects bending moment to bending stress. A larger section modulus reduces stress for the same applied moment.
Is this enough for final design?
No. Use it for preliminary checks only. Final design should include codes, combinations, connections, bracing, bearing, and professional review.