DOWNLOAD PDF
### INTRODUCTION

Beam theory or beam deflection is such a common engineering fundamental; it is impossible to be omitted from almost any engineering-specialism. However this sheet incorporates stress and stiffness as well.

From various load cases; the following beam theory equations are given:

- beam deflection (sag)
- beam curvature
- reaction force
- shear force
- reaction moment
- stress
- stiffness

**Load case**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**For: 0≤x≤a**

**Curvature **

**Sag **

only if a>b

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**For: a≤x≤L**

**Curvature **

**Sag **

only if a<b

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**For: 0≤x≤a**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**For: a≤x≤L**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**For: 0≤x≤a**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**For: a≤x≤L**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**For: 0≤x≤a**

**Curvature **

**Sag **

Only if a 0,414L

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**For: a≤x≤L**

**Curvature **

**Sag **

Only if a 0,414L

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**For: 0≤x≤a**

**a<b**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**For: a≤x≤L**

**a>b**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

}

**Load case**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

**Stress **

**Stiffness **

**Load case**

**Curvature **

**Sag **

**Reaction force **

**Shear force **

**Reaction moment **

resp.

resp. L

**Stress **

**Stiffness **

**Cross section**

**Area moment of inertia **

**Cross section**

**Area moment of inertia **

**Cross section**

**Area moment of inertia **

**Cross section**

**Area moment of inertia **

This page uses QuickLaTeX to display formulas.