Coconote
AI notes
AI voice & video notes
Export note
Try for free
Shear and Moment Diagrams: An Introduction
Jul 16, 2024
🤓
Take quiz
🃏
Review flashcards
Shear and Moment Diagrams: An Introduction
Internal Forces (V and M)
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
Plotting Shear Force and Bending Moment
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
Key Concepts:
Related Graphs
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
Problem Solving Steps
Step 1: Global Equilibrium
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
Step 2: Discontinuities
Identify and draw discontinuities where loads change (concentrated loads, boundary conditions)
Correct discontinuities back to distributed loads if required for accurate plotting
Step 3: Plotting the V Diagram
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
Tips for Accurate Graphing
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
Plotting the 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
Conclusion
Maximum Shear Force: 16 kN
Maximum Bending Moment: 28 kN.m
Importance of consistent and careful plotting for designing safe structures
Next Steps
Look forward to advanced topics like concentrated moments in future presentations
📄
Full transcript