Beam Capacity Checking

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Description

Core Engineering Principle: Concrete Beam Moment Resistance

This calculation follows the principle that in a reinforced concrete beam, concrete resists compression while steel reinforcement resists tension, and the beam's strength depends on achieving equilibrium between these forces.

1. Force Equilibrium Concept

  • When a concrete beam bends, the top portion goes into compression (concrete handles this well)
  • The bottom portion goes into tension (concrete is weak here, so steel rebar is needed)
  • For the beam to be stable: Compression Force = Total Tension Force
  • This is expressed as: C = T₁ + T₂ + T₃ (sum of all tension forces)

2. Stress Block Method

  • The calculation uses the "equivalent rectangular stress block" - a simplified way to represent the actual curved stress distribution in concrete
  • The concrete compression is calculated as: C = 0.85 × f'c × a × b
  • Where 'a' is the depth of the equivalent compression block

3. Multi-Layer Reinforcement Analysis This beam has steel bars at different depths (layers), which affects capacity:

  • Different grades of steel (Grade 40 vs Grade 60) have different yield strengths
  • Different positions (closer to or farther from the compression zone) contribute differently to moment resistance
  • Each layer contributes: T = As × fy (steel area × yield strength)

4. Moment Arm Principle

  • The moment capacity depends not just on the forces, but on their lever arms (distances)
  • Each tension force creates moment: M = T × (distance from compression center)
  • Total moment = sum of all individual contributions

5. Tension-Controlled Verification

  • The calculation checks that the steel yields before concrete crushes
  • This ensures ductile failure (steel stretches and gives warning) rather than brittle concrete failure
  • The fs > 1000 MPa check confirms the beam will fail safely

6. Design Comparison

  • The "Actual Beam" represents an existing or proposed reinforcement layout
  • The "Designed Beam" represents a simplified alternative arrangement
  • Comparing their capacities determines if the actual beam is adequate

This is like comparing two different arrangements of support cables in a suspension system - you need to ensure the actual arrangement can handle at least as much load as your minimum design requirement.

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Jeremy Mendoza (jj4321)
17 Jun 2025
File Size: 153
Downloads: 8
File Version: 1.0
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Comments: 1
johndoyle-admin 22 hours ago
Thanks for your debut contribution I have awarded you a 3 month XLC Pro subscription by way of thanks!
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