Simply Supported Beam Calculator
Calculate bending stress, deflection, slope, and bending moment for simply supported beams under point or distributed loads. Step-by-step solutions included.
simply supported beam calculator:
Calculate bending stress, deflection, slope, and maximum bending moment for and-supported beams using this Supported Beam Calculator. Enter the span length, load, cross-section, and the material properties. Midspan deflection, support slop, and distribution of bending moment are demonstrated using step-by-step calculations.
Shaft Design Tool Formula:
Equivalent Radial Load (P):
\[ d = \sqrt{[(16/\pi.S_{s}). \sqrt{(M^{2}+(T.K)^{2})}]} \]
(where d = shaft diameter, Ss = allowable shear stress, M = bending moment, T = torque, K = shock/load factor)
The Shaft Design Calculator is used by engineers and students as well as technicians in the design and analysis of rotating shafts in mechanical systems. Shafts are used to pass the motors, the bending moments, the axial forces of the rotating machinery, the gears, the pulleys, and the rotating machines. Designing the shaft properly is safe, reliable, and has a long life of operation.
Torque, bending moment, axial load, material yield/ultimate strength, and desired factor of safety of the user can be entered. The calculator can be used to determine bending stress, torsional stress, combined stress (Von Mises stress or Goodman), and recommended shaft diameter. Formulas to compute torsion, bending, and combined stress are presented in a form of step-by-step form, and it is easy to optimize the design of a shaft to be strong, stiff, and safe.
SI units are accepted: N, kN, mm, MPa, RPM. The tool is most suitable with mechanical engineers, design engineers, students, and educators dealing with motors, gearboxes, conveyor systems, and rotating machinery to properly and safely dimension and stress analyze shafts.
⚡ Work & Installation Input to Output:
Input:
- Torque (T)
- Bending moment (Mb)
- Axial load (Fa)
- Material yield/ultimate strength (σy / σu)
- Desired factor of safety (FOS)
- Units: N, kN, MPa, mm, RPM
Processing:
- Compute bending stress: σb = 32 Mb / (π d^3)
- Compute torsional stress: τ = 16 T / (π d^3)
- Compute combined stress: σeq = √(σb^2 + 4τ^2) (Von Mises)
- Compute required shaft diameter: d = function of applied loads and allowable stress
- Apply factor of safety to validate design
- Optional: check axial stress contribution and Goodman criteria
Output:
- Bending stress (σb)
- Torsional stress (τ)
- Equivalent combined stress (σeq)
- Recommended shaft diameter (d)
- Step-by-step formulas and calculations
Testing and Final Adjustments
Test common scenarios:
- Shaft with T = 500 N·m, Mb = 2000 N·m → compute τ, σb, σeq, and diameter
- Axial load Fa = 1000 N → include in combined stress check
- Edge cases: zero bending, high torque, very high factor of safety
- Units validation: N ↔ kN, MPa ↔ N/mm²
- Step-by-step clarity for students and engineers
- Mobile/desktop UX: numeric keypad, labels, error messages
- Include standard steel and alloy materials with yield/ultimate strength references
- SEO metadata: "Shaft Design Calculator," "Bending Stress," "Torsional Stress," "Shaft Diameter," schema markup
Frequently Asked Questions - Simply Supported Beam Calculator:
What is a simply supported beam?
A simply supported beam rests on two supports and is free to rotate at the ends, commonly used in bridges and floors.
How do I calculate maximum bending moment?
For point load at midspan: M_max = P × L / 4; for uniform load: M_max = w × L² / 8.
How do I calculate maximum bending stress?
σ_max = M_max × y / I, where y is distance from neutral axis, I is moment of inertia.
How do I calculate maximum deflection?
Point load: y_max = P × L³ / (48 × E × I); Uniform load: y_max = 5 × w × L⁴ / (384 × E × I).
How do I calculate slope at supports?
Point load: θ_max = P × L² / (16 × E × I); Uniform load: θ_max = w × L³ / (24 × E × I).
Which units are supported?
Lengths in meters or mm, forces in N, modulus E in Pa/MPa, stress in Pa/MPa.
Can it handle rectangular and circular beams?
Yes, it supports rectangular, circular, and I-section beams.
Is step-by-step solution available?
Yes, formulas and calculations are displayed step-by-step.
Can it plot bending moment and deflection diagrams?
Yes, optional plotting along the beam length is available.
Who should use this calculator?
Structural and mechanical engineers, students, educators, and designers analyzing simply supported beams.
