Beam Flange Stresses

Core Engineering Principle: Local Flange Bending Under Concentrated Loads

This calculation follows the principle that when a concentrated wheel load from a crane trolley acts on a girder flange, it creates localized bending stresses that are much higher than the general beam bending stresses.

1. Stress Concentration Effect

• When a wheel applies load to a flange, the load doesn't spread out evenly
• The flange acts like a small plate supported by the web, creating local bending
• This localized bending produces stress "hot spots" that can be much higher than the overall beam stress

2. Critical Point Analysis The calculation examines stress at three critical locations:

• Point 0: At the flange-to-web junction (where support occurs)
• Point 1: Directly under the wheel contact point (maximum loading)
• Point 2: On the opposite side of the flange (tension/compression reversal)

3. Empirical Stress Coefficients

• The complex equations with coefficients (Cx0, Cx1, Cy0, Cy1) are empirically-derived formulas
• These come from extensive testing and finite element analysis by CMAA (Crane Manufacturers Association of America)
• They account for the complex 3D stress distribution around the wheel contact point

4. Load Distribution Consideration

• The parameter "ph" relates to how close the wheel is to the flange edge
• Wheels near the edge create higher stress concentrations
• The calculation includes impact factors since crane loads are dynamic

5. Combined Stress Analysis

• The local wheel stresses are combined with the overall beam bending stresses
• This ensures the total stress doesn't exceed material limits
• Different factors are applied for single web vs. box sections

This is essentially analyzing the same phenomenon that occurs when you step on a diving board - the local area under your foot experiences much higher stresses than the board as a whole, and these must be checked separately to prevent local failure.