What Is the Timoshenko Beam Shear Deformation & Deflection Calculator?
Timoshenko beam theory relaxes the Kirchhoff assumption that plane sections remain normal to the neutral axis, allowing cross-sections to rotate due to shear.
How Does the Timoshenko Beam Shear Deformation & Deflection Calculator Work?
Sums classical flexural curvature deflection with shear strain deflection proportional to shear coefficient k = 5/6 for rectangular cross-sections.
Timoshenko Beam Shear Deformation & Deflection Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
w_{ ext{total}} = rac{P L^3}{48 E I} + rac{P L}{4 k G A}, quad k = rac{5}{6} approx 0.833
Timoshenko beam deflection: pure bending term plus transverse shear term.
How to Use the Timoshenko Beam Shear Deformation & Deflection Calculator
- Input load in kN, span length in meters, width and depth in mm, and elastic moduli E and G.
Step-by-Step Example Calculation
Short Deep Structural Steel Beam
Input Values:
loadKn:60
lengthM:1.8
widthMm:120
heightMm:280
youngsModulusGpa:210
shearModulusGpa:80
Worked Steps: Bending deflection = 0.654 mm, Shear deflection = 0.121 mm (18.5% shear contribution), Total = 0.775 mm.
Understanding Your Result
Shows total deflection, pure bending component, shear component, and percentage shear contribution.
Factors That Affect the Result
- As span-to-depth ratio L/h drops below 10, shear deformation becomes significant (exceeding 10–20% of total deflection).
When Should You Use This Calculator?
- Designing transfer girders, stub cantilevers, composite sandwich core beams, and heavy machinery bolsters.
Assumptions & Limitations
- Applies to linear elastic isotropic simply supported rectangular beams.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard first-order shear deformation beam theory.