What Is the Timoshenko Beam Shear Deformation Deflection Calculator?
Timoshenko beam theory relaxes the Kirchhoff assumption, allowing cross-sections to rotate independently of the slope of the deflection curve due to shear strain.
It provides superior accuracy for stocky beams, high-frequency vibrations, and sandwich panels.
How Does the Timoshenko Beam Shear Deformation Deflection Calculator Work?
Calculates pure flexural bending deflection delta_b = P*L^3 / (48*E*I).
Calculates transverse shear deflection delta_s = P*L / (4*kappa*A*G).
Sums components to yield total Timoshenko deflection and calculates shear percentage.
Timoshenko Beam Shear Deformation Deflection Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Superposition of Euler bending compliance and Timoshenko transverse shear compliance.
How to Use the Timoshenko Beam Shear Deformation Deflection Calculator
- Enter beam span length and concentrated point load.
- Enter Young's modulus E, shear modulus G, moment of inertia I, and cross-section area A.
- Set shear correction factor kappa (default 5/6 for rectangular sections).
Step-by-Step Example Calculation
Heavy Machine Foundation Deep Steel Girder
Input Values:
Understanding Your Result
In slender beams (L/h > 20), shear deflection is under 1% of total deflection and can be neglected.
In deep beams (L/h < 5), shear deflection can contribute 15% to 40% of total deflection.
Factors That Affect the Result
- Span-to-depth ratio (L/h): Shear deformation scales with (h/L)^2 relative to bending.
- Cross-section shape: I-beams experience concentrated shear in the web, requiring kappa ~ A_web / A_total.
When Should You Use This Calculator?
- Structural design of bridge pier transfer girders and foundation pile caps.
- Fiber-reinforced composite laminates where shear modulus G is very low relative to axial modulus E.
Assumptions & Limitations
- Applies to simply supported beam with center concentrated point load.
- Assumes linear elastic material behavior.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard Timoshenko beam solution universally implemented in structural FEA solvers.