Calculate support reactions, total load, maximum shear, and maximum bending moment for common beam load cases. Use this as the first step before checking bending stress, beam deflection, section modulus, and machine frame stiffness.
Select a load case and enter the span, load, and load position. The calculator returns reactions, total load, maximum shear, and maximum bending moment.
Beam reactions and maximum moment are usually the first calculations in a structural check. They tell you how much force the supports must carry and how much bending the member must resist.
Reactions estimate the force pushed back into supports, bolts, welds, bearings, brackets, and machine-frame mounting points.
Maximum moment is the key input for bending stress. The larger the moment, the more the beam wants to bend or yield.
Maximum shear helps identify the largest vertical force near a support or fixed end. It is not a complete shear stress design, but it is useful for practical machine checks.
These are simplified common load cases. More complex machine structures may need combined loads, torsion, finite element analysis, or formal engineering review.
Simply Supported, Center Point Load:
RA = P / 2
RB = P / 2
Mmax = P × L / 4
Simply Supported, Off-Center Point Load:
RA = P × (L - a) / L
RB = P × a / L
Mmax = P × a × (L - a) / L
Simply Supported, Uniform Load:
Total Load = w × L
RA = w × L / 2
RB = w × L / 2
Mmax = w × L² / 8
Cantilever, End Point Load:
Fixed Reaction = P
Mmax = P × L
Cantilever, Point Load at Distance:
Fixed Reaction = P
Mmax = P × a
Cantilever, Uniform Load:
Total Load = w × L
Fixed Reaction = w × L
Mmax = w × L² / 2
Do not start with deflection or stress until the load case makes sense. The load path comes first.
Decide whether the member is simply supported, cantilevered, point loaded, uniformly loaded, or carrying multiple concentrated loads.
Use the maximum bending moment as the main input for checking bending stress and comparing section modulus.
Strength is not enough. A machine member can be below yield stress and still flex enough to cause alignment, sensor, robot, or tooling problems.
If stress or deflection is too high, compare tubes, bars, shafts, and plates using section modulus and moment of inertia.
Picking the closest load case matters. The same total weight can create very different support reactions and bending moments depending on where the load is applied.
Use this when one concentrated load is near the middle of a beam supported at both ends.
Use this when a motor, cylinder, gearbox, bracket, tooling nest, or fixture load is closer to one support than the other.
Use this for distributed weight such as plates, guarding, light conveyors, trays, or evenly supported machine components.
Use this for two mounted components on the same rail or beam, such as two cylinders, two tooling stations, or two support loads.
Use this for overhung brackets, tooling arms, sensor mounts, extended shafts, or unsupported machine details.
Use this for a cantilevered member with weight spread over the full length, such as a guard, tray, cover, or extended support.
If reactions or moments are higher than expected, the best fix is often geometry, not just stronger material.
Beam reactions are the first step. Use these related tools to finish the mechanical design check.
Use maximum bending moment to estimate bending stress and safety factor against yield.
Open Bending Stress →Check whether the member bends too much under load, even if stress is acceptable.
Open Beam Deflection →Calculate I and S values for rectangles, shafts, tubes, and custom sections.
Open Section Modulus →Check whether mounting bolts provide enough clamp load for brackets and supports.
Open Clamp Load →Check bearing life when beam loads feed into shafts, rollers, or rotating supports.
Open Bearing Life →Return to the full structural and mechanical sizing workflow.
Open Machine Design Hub →Reactions and maximum moment tell you where the force goes. Once those are known, check bending stress, deflection, section properties, fasteners, and supports.