SFD and BMD in Structural Mechanics
Master the internal forces of beams. Learn where shear is most dangerous and why bending moment determines the amount of steel rebar.
The Internal Struggle of a Beam
When you sit on a bench, the wood doesn't just bear your weight; it internally resists being sliced and being bent.
1. Shear Force (SF): The vertical force that tries to slice the beam like a pair of scissors. It is usually highest near the supports.
2. Bending Moment (BM): The internal torque that tries to curve the beam. It is usually highest in the middle of a span.
Standard Equations
Interpreting the Diagrams
- Shear Force Diagram (SFD): Shows where the beam is most likely to fail by "Punching Shear." Engineers use Stirrups (lateral ties) to resist these forces.
- Bending Moment Diagram (BMD): Shows where the beam will "Sag" (tension at bottom) or "Hog" (tension at top). This determines where the main thick longitudinal rebar must be placed.
- Point of Zero Shear: The location where the Shear Force is zero is almost always the location of the Maximum Bending Moment.
Cantilever vs. Simply Supported
In a Simply Supported beam, the bottom of the beam stretches (tension) and the top squishes (compression). This is why rebar is at the bottom.
In a Cantilever beam (like a balcony), the top stretches and the bottom squishes. Therefore, the main reinforcement must be placed at the TOP of the beam.
Frequently Asked Questions (FAQ)
What is 'Hogging' and 'Sogging'?
Sagging (Positive Moment) occurs when a beam curves like a smile, creating tension at the bottom. Hogging (Negative Moment) occurs when it curves like a frown (typical over supports in continuous beams or cantilevers), creating tension at the top.