Jul 16, 2024

- Internal forces in beams: Shear Force (V) and Bending Moment (M)
- Importance: Knowing the value of V and M at every point for beam design

- To determine V and M across a beam, graph them along the beam's length
- Purpose: Identifying maximum shear force and bending moment for safe design

- V and M graphs should be aligned vertically; each graph is the integral of the one above it:
- Load Curve
- Shear Force Curve
- Bending Moment Curve

- Order of Lines:
- Concentrated Load -> Horizontal Line -> Slope -> Parabolic -> Cubic

- Identify support reactions (e.g., pin, roller)
- Calculate reaction forces:
- Sum of Forces = 0
- Sum of Moments = 0

- Example: Problem with 18 kN, 12 kN, and 6 kN loads over discrete intervals
- Solve for reaction forces at supports: B_Y and A_Y

- Identify and draw discontinuities where loads change (concentrated loads, boundary conditions)
- Correct discontinuities back to distributed loads if required for accurate plotting

- Plot the shear force (V) across the beam:
- Start from zero, apply loads, and maintain the integral relationship
- Ensure summation returns to zero at the end

- Example values are given to illustrate the change in V across intervals

- Ensure all calculations are correct; discrepancies indicate mistakes in global equilibrium
- Analysis through analogy (walking across the beam with a backpack): load additions affect the shear force step by step
- Mark plus/minus to indicate the upward/downward slope on M diagram

- Areas under V diagram give moments:
- Height in kN and width in meters
- Area calculated as ": height * width = kN * meter = moment"

- Plot Bending Moment (M) based on area calculations, ensuring slope consistency
- Example: Plot calculations for specific beam segments, e.g., 28, 40, 12 kN.m

- Ensure bending moment also returns to zero, validating correctness

- Maximum Shear Force: 16 kN
- Maximum Bending Moment: 28 kN.m
- Importance of consistent and careful plotting for designing safe structures

- Look forward to advanced topics like concentrated moments in future presentations