CTC 422 Design of Steel Structures

1
CTC 422Design of Steel Structures

• Beams
• Shear and Deflection

2
Beam Design

• Student Objectives
• Analyze a beam to calculate load, shear, moment
  and deflection and to determine if a given beam
  is adequate
• Design (select) a beam to safely to support a
  load considering moment, shear and deflection

3
Design for Shear - LRFD

• Steel beams ? Shear seldom governs
• Exceptions
• Very short spans
• Very heavy loads
• Normal procedure
• Select beam for moment (bending)
• Then check for shear

4
Load and Resistance Factor Design - LRFD

• Design strength Required strength
• FRn Ru
• For shear
• Fv Vn Vu
• Where
• Vn Nominal shear strength
• Fv Strength reduction factor for shear
• Vu Required shear strength based on factored
  loads

5
Design for ShearChapter G of AISC Code

• Nominal shear strength, Vn, depends on the
  failure mechanism of the beam
• Beam can fail by
• Shear yielding
• Shear buckling
• Can be inelastic or elastic buckling
• Failure mechanism is related to the width to
  thickness ratio of the beams web, h / tw
• Section G 2.1 applies to doubly symmetric
  sections (W, M, S and HP shapes) and channel
  shapes (C and MC)
• Section G 2.1a applies to I-shaped sections with
  h / tw a given limit
• Section G 2.1b applies to other doubly symmetric
  shapes and channels
• Nominal shear strength in this case is less than
  calculated by G 2.1a

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Design for ShearChapter G of AISC Code

• Nominal shear strength, Vn, can be calculate by
  Section G 2.1a, or G 2.1b
• Then check FvVn Vu
• Or, shear strength FvVn tabulated in design aids
  can be used
• Shear strength is listed in the following tables
• W-Shapes Table 3-2
• Also listed in Table 3-6
• S-Shapes Table 3-7
• Channel Shapes (C and MC) Tables 3-7 and 3-8

7
SeviceabilityChapter L of AISC Code

• Deflection Section L3
• Deflections under service load combinations shall
  not impair the serviceability of the structure
• Limits on deflections are specified in building
  codes
• NYS Building Code Section 1604.3
• Floor members
• Live load deflection span / 360
• Dead load plus live load deflection span / 360
• ACI Masonry Code
• Beams supporting masonry
• Total deflection span / 600 0.3 inches
• Very stringent criteria

8
Deflections

• Beam deflections for various load conditions
  shown in table 3-23
• For a simply supported beam with a uniform load
  on its full span
• ? 5wL4 / 384EI
• Use consistent units, usually kips and inches
• If load, w, and span, L, are known this equation
  can be solved for the moment of inertia, I, that
  would produce a given deflection
• For ? span / 360, I wL3 / 43
• For ? span / 240, I wL3 / 64.5
• For ? span / 600, I wL3 / 25.8
• In these equations, w is in kips / ft, L in feet,
  and I in in4
• Approximate deflection in beams with non-uniform
  loads
• Calculate the equivalent uniform load based on
  moment
• E.U.L 8 M / L2
• Use this value for w in the equations above