Project: Cantilever Beam Analysis (Klaus Building Awning)

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The objective was to perform a static structural analysis on a cantilevered glass canopy located at the Klaus Advanced Computing Building on the Georgia Tech campus.

• System: A 3-meter cantilever beam fixed at one end (Point A).
• Loads:
  
  • The structure's self-weight ($W = 1000 N$) modeled as a concentrated load at the centroid.
  • An external tip load ($F = 50 N$) representing maintenance equipment or wind/snow load.

To solve for the unknown reaction forces, I isolated the beam from its surroundings.

• Boundary Conditions: modeed Point A as a Fixed Support, constraining movement in the X and Y directions and preventing rotation.
• Reactions: Solved for Vertical Reaction ($A_y$), Horizontal Reaction ($A_x$), and the Reaction Moment ($M_A$).

Applying Newton's First Law for a body in static equilibrium (F = 0, M = 0), I calculated the internal forces required to keep the awning stable.

Governing Equations:

• Sum of Vertical Forces:
  
  F_y = A_y - 1000N - 50N = 0, A_y = 1050 N
• Sum of Moments about A:
  
  M_A = M_A - 1000N(1.5m) - 50N(3m) = 0, M_A = 1650 N

Shear & Bending Moment Diagrams:

I constructed V and M diagrams to visualize how internal forces change along the length of the beam.

• Shear (V): The maximum shear force of 1050 N occurs at the support connection.
• Moment (M): The maximum bending moment is 1650 N at the wall. This indicates that the connection at Point A is the critical failure point and requires the most robust reinforcement.

• Simplification: Successfully modeled a complex distributed load (weight of the glass) as a point load at the center of mass for reaction analysis.
• Critical Points: Identified that the anchoring bolts at the wall (Point A) must withstand a moment of $1650 N\cdot m$, guiding fastener selection.