Structural Engineering: Brackets and Corbels

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Questions and Answers

What is the value of the total shear friction steel (Avf)?

  • 644 mm²
  • 1116 mm² (correct)
  • 1055 mm²
  • 626 mm²

How is the nominal tensile strength area (An) determined?

  • By calculating $\dfrac{N_{uc}}{∅f_y}$ (correct)
  • By using the formula for steel area at a certain depth
  • Using shear strength equations
  • By taking the average of two areas

What is the value of the bending moment (Mu) calculated in the given content?

  • 625 KN.m
  • 71 KN.m (correct)
  • 98 KN.m
  • 492 KN.m

When determining the shear area (Asc), what is the minimum requirement?

<p>Asc must be greater than or equal to $\dfrac{A_{uf}+A_n}{2}$ (D)</p> Signup and view all the answers

What is the final area of the top bracket rebar (Asc) after checking requirements?

<p>1055 mm² (D)</p> Signup and view all the answers

What is the primary purpose of brackets in structural engineering?

<p>To support concentrated loads from beams or slabs. (A)</p> Signup and view all the answers

Which type of failure is characterized by poor detailing of the embedded length?

<p>Type 1 Shear Failure (A)</p> Signup and view all the answers

What governs the design of brackets and corbels according to their behavior?

<p>Shear forces (B)</p> Signup and view all the answers

What is a Strut-and-tie model (STM) used for in the context of brackets and corbels?

<p>To better capture load transfer mechanisms. (A)</p> Signup and view all the answers

What issue may arise from having a small thickness of a corbel?

<p>Type 2 Shear Failure (C)</p> Signup and view all the answers

In the design of brackets, what role do the top bars at the column face play?

<p>They transfer bending moments to vertical members. (B)</p> Signup and view all the answers

What must be carefully considered to avoid shear failure in brackets?

<p>Amount of stirrups provided. (D)</p> Signup and view all the answers

Why is horizontal tension reinforcement necessary in brackets and corbels?

<p>To resist horizontal forces from bending moments. (A)</p> Signup and view all the answers

What is the maximum allowed span ratio for using the flexural model in bracket design?

<p>av/d ≤ 1 (D)</p> Signup and view all the answers

Which equation represents the nominal shear strength for normal weight concrete?

<p>$V_n = rac{0.2 fc bd}{(3.3+0.08 fc) bd}$ (C)</p> Signup and view all the answers

Under what condition must a horizontal tensile force be assumed in bracket design?

<p>Nue ≥ 0.2 Vu (D)</p> Signup and view all the answers

What is the appropriate equation to calculate the area of steel required to resist moment Mu?

<p>$A_f = rac{Mu}{φf_y(d-a/2)}$ (D)</p> Signup and view all the answers

Which of the following is NOT a condition for determining the total area required for flexure and direct tension at the top of the bracket?

<p>$A_sc = A_f + A_n - A_{vf}$ (B)</p> Signup and view all the answers

What is the minimum area of closed hoop stirrups required in relation to the area of the tensile reinforcement?

<p>$A_h ≥ 0.5(A_sc - A_n)$ (D)</p> Signup and view all the answers

What is the recommended friction factor (μ) for normal weight concrete?

<p>1.4 (D)</p> Signup and view all the answers

Which material strengths are cited for the example in designing the bracket?

<p>f'c = 35 MPa and f''y = 420 MPa (D)</p> Signup and view all the answers

Flashcards

Brackets and Corbels

Short cantilevers projecting from columns or walls to support loads, behaving differently from conventional beams due to their short span, high forces, and deep section.

Bracket

A short cantilever supporting concentrated loads, often projecting from columns or walls.

Corbel

A short cantilever projecting from a column or wall, typically deeper than a bracket, transferring loads from horizontal members to vertical members.

Shear-controlled Design

Design primarily focused on resisting shear forces, due to high shear in brackets and corbels.

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Strut-and-Tie Model (STM)

Analysis and design method capturing the load transfer mechanism in brackets and corbels, better than conventional methods.

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Horizontal Tension Reinforcement

Reinforcement needed to resist horizontal forces arising from bending moments and enabling crack control in brackets and corbels.

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Flexural Failure

Bracket failure mode due to insufficient main steel or incorrect cantilever consideration (av/d ≤1).

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Diagonal Splitting

Bracket failure mode due to low compressive strength relative to high main steel, or insufficient steel across the strut.

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Shear Failure

Bracket failure mode due to insufficient stirrups or incorrect shear behavior consideration (av/d ≤1).

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ACI 318 Code

Provides guidelines for designing brackets and corbels.

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Shear force (Vu)

The maximum shear force the structural element can withstand

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Normal shear strength (Vn)

The shear strength based on material properties.

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Ultimate Bracket Load (Vu)

Maximum load a bracket can endure without failure.

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Steel Area (A vf)

Required area of shear friction steel to resist shear.

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Nominal Tensile Strength (An)

Required area of steel to resist tensile forces.

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Total Steel Area (Asc)

Total area of steel reinforcement at a support.

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Minimum Reinforcement Area (Asc_min)

Lower limit area for reinforcement for compression.

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Bending Moment (Mu)

Calculated moment associated with bracket load, supporting members and/or reaction.

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Flexural Compression Stress Block Depth (ca)

Depth of compression zone in beam calculations.

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Additional Steel Area (Ap)

Supplementary steel needed for bending resistance.

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Stirrup Area (Ah)

Area needed for shear stirrups in a beam.

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Bracket Design variables

Parameters considered in the design of structural bracing elements.

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Reinforcement Selection

Choosing the size and number of bars required for adequate strength and serviceability criteria.

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Span Ratio (av/d ≤ 1)

Indicates when to use flexural model for bracket design. If the span ratio (av/d) is less than or equal to 1, use the flexural model.

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Span Ratio (a/d ≤ 2)

Indicates when to use strut-and-tie model for bracket design. If the ratio (a/d) is less than or equal to 2, use the strut-and-tie model.

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Bearing Depth (t ≥ 0.5d)

Minimum depth requirement for the bearing area of the bracket.

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Strength Check (Mu ≤ ØMn and Vu ≤ ØVn)

The factored moment (Mu) and shear force (Vu) must be less than or equal to the factored moment capacity (ØMn) and shear capacity (ØVn) respectively, to ensure the bracket doesn't fail.

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Horizontal Tensile Force (Nue ≥ 0.2 Vu)

In the absence of a roller or low-friction support pad, the horizontal tensile force (Nue) assumed must be at least 20% of the factored shear force (Vu).

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Shear Capacity (Vn)

Equation to calculate the nominal shear capacity of the bracket.

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Steel Area for Moment Resistance (Af)

Formula for calculating the steel area required to resist the moment (Mu).

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Nominal Tensile Steel Area (An)

Steel area for direct tension.

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Total Steel Area for Flexure and Tension (Asc)

Minimum total steel area at top of the bracket.

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Hoop Stirrup Area (Ah)

Minimum hoop stirrup area to control diagonal tension.

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Shear-Friction Reinforcement (Avf)

Formula for calculating the steel area required for shear-friction reinforcement.

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Additional Steel Area (Asc ≥ 0.04(fc/fy)bd)

Ensure a minimum steel area (Asc) for strength and ductility.

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Study Notes

Introduction

  • Brackets and corbels are short cantilever beams
  • They project from columns or walls
  • Support loads like beams or slabs
  • Structural behavior differs from conventional beams
  • Short span, large applied forces (high shear stresses)
  • Deep section relative to their length
  • ACI 318 code provides design guidelines

Brackets

  • Short cantilevers used to support concentrated loads
  • Usually project from columns or walls

Corbels

  • Short cantilevers extending from columns or walls
  • Typically deeper in section
  • Transfer loads from horizontal members (beams) to vertical members (columns)

Failure Modes

  • Causes of failure include:
    • Small amount of main steel
    • Low compressive strength with high main steel
    • Small amount of reinforcement crossing the strut
    • Small amount of stirrups
    • Loss of anchorage
    • Lack in the detailing of embedded length
    • Small thickness of corbel
    • High value of horizontal load
    • Lack in the seat plate detailing

Behavior of Brackets and Corbels

  • Experience high shear forces and moments
  • Shear-controlled design (shear force often governs the design)
  • Strut-and-tie models (STM) used for analysis and design to capture load transfer mechanisms
  • Horizontal tension reinforcement needed to resist horizontal forces
  • Provide additional capacity for crack control

Design Considerations

  • Bracket considered as a short cantilever with flexural tension at column face
  • Strut and tie model for performance analysis
  • Span ratio (av/d) ≤ 1 and (a/d) ≤ 2 determine design method (flexural/strut and tie)
  • Depth at the outside edge of bearing area (t ≥ 0.5d)
  • Mu ≤ ØMn and Vu ≤ ØVn with Ø=0.75
  • Horizontal tensile force must be considered without roller/low-friction support pad
  • Find d according to specified formulas

Additional Calculations

  • Calculations involve finding the amount of steel (A) required to resist moment (Mu), area of steel (An) for nominal tensile strength and shear-friction reinforcement (Av)
  • Total area required for flexure and direct tension
  • Closed hoop stirrups (Ah) area should be greater than 0.5(Asc - An), 0.5 Af, and Avf / 3
  • Example calculations for column bracket with end reaction and vertical load specifications for specific material strengths.

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