W18x46 Beam Capacity: Concentrated Load, 16ft Span, A992 Steel

Problem Statement:

• Beam: W18×46, A992 steel
• Span: 16 ft (simply supported with lateral support at compression flange at ends only)
• Load: Concentrated service live load
• Load Location: 4 ft from the left support
• Bearing Length at Supports: 4 inches
• Bearing Length at Load: 8 inches
• Bearing Plate Thickness: 3/4 inch
• Neglect beam weight

Solution:

• Moment Calculation:
  • The maximum moment due to a concentrated load on a simply supported beam occurs at the load point.
  • Using the formula for the moment at a point load on a simply supported beam:
    • where:
      • P = Concentrated load
      • a = Distance from left support to load = 4 ft
      • b = Distance from right support to load = 12 ft
      • L = Span of the beam = 16 ft
    • ft-kips
• Section Modulus:
  • Look up the section modulus ( ) for a W18×46 beam in the AISC Steel Construction Manual.
  • For a W18x46,
• Nominal Flexural Strength (M_n):
  • where:
    • = Yield strength of A992 steel = 50 ksi
• Design Flexural Strength (φM_n):
  • = 0.9 (for flexure)
• Maximum Load Capacity (P_bending):
  • Equate the maximum moment due to the load to the design flexural strength:

• Shear Force Calculation:
  • The maximum shear force in a simply supported beam with a concentrated load occurs at the support closer to the load.
  • kips
• Nominal Shear Strength (V_n):
  • where:
    • = Area of the web =
    • d = Depth of the beam (from AISC manual) = 18.0 in
    • = Web thickness (from AISC manual) = 0.415 in
    • = Shear coefficient (from AISC manual, typically 1.0 for beams without stiffeners)
• Design Shear Strength (φV_n):
  • = 1.0 (for shear)
• Maximum Load Capacity (P_shear):
  • Equate the maximum shear force due to the load to the design shear strength:

• Bearing Strength at Support:
  • Check the web crippling at the support with the smaller bearing length (4 inches).
  • where:
    • N = Bearing length at support = 4 in
    • = Flange thickness (from AISC manual) = 0.695 in
• Design Bearing Strength at Support (φR_n):
  • = 0.75 (for web crippling)
• Maximum Load Capacity at Support (P_crippling_support):
  • Since the reaction at each support is half the total load:
• Bearing Strength at Load Point:
  • Repeat the above calculations for the bearing length at the load point (8 inches).
  • You’ll find that the bearing strength at the load point is significantly higher than at the support, so it won’t govern the design.

• Bearing Yield Strength:
• Design Bearing Yield Strength (φR_n):
  • = 1.0 (for local yielding)
• Maximum Load Capacity at Support (P_yielding_support):
  • Since the reaction at each support is half the total load:

Conclusion: