L2 - Moment Design.pdf

CHAPTER 2 MOMENT DESIGN /
FLEXURE DESIGN
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DESIGN METHOD / PROCEDURES
Based on Section 6.1 MS EN 1992-1-1 – ULS analysis
and design of section subjected to bending
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In this chapter, you’ll learn
about:
 Rectangular section: Singly and doubly
reinforced
 Flanged section: Singly and doubly
reinforced
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Two different types of problems
in the study of RC flexural
elements:
 (1) Design:
 Given a cross-section, concrete strength, steel
reinforcement strength, and applied ultimate bending
moment, determine the area and number of
reinforcement required.
 (2) Design Check:
 Given a cross-section, concrete strength, number, strength
and size of steel reinforcement provided, determine the
moment of resistance.
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Which one is T, L, & Rectangular?
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Stress Block Diagram
S = 0.8x
𝑓𝑐𝑑 = 0.567𝑓𝑐𝑘
𝜇 = 1.0
Lecture 1, slide 35
𝑓𝑦𝑑 = 0.87𝑓𝑦𝑘
Lecture 1, slide 38
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Singly Reinforced Section
Stress Area
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(to avoid sudden failure)
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Example 1: Solution
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Example 2: Solution
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Doubly Reinforced Section
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Stress in Compression Reinforcement
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Stress in Compression Reinforcement
(a reduced stress should be used)
Reduced stress formula
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Example 3: Solution
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Example 4: Solution
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 The plastic behavior of reinforced concrete at the ULS affects
the distribution of moments in a structure.
 To allow for this, the moment derived from an elastic analysis
may be redistributed based on the assumption that plastic
hinges have formed at the sections with the largest moments.
 Formation of plastic hinges required relatively large rotations
with yielding of the tension reinforcement.
 To ensure large strain in the tension steel, the code of practice
restricts the depth of the neutral axis to correspond with the
magnitude of the moment redistribution carried out.
Moment REDistribution
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Plastic Hinges
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Moment Distribution
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Moment Distribution
Prove this equation!
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Derivation of z Equation
(S = 0.8x)
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Simplified EC2 Method
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Example 5: Solution
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Flanged Beam/Section
A portion of slab act integrally with the beam
in longitudinal direction.
WEB
WEB
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 When the flange is relatively wide, the flexural
compressive stress is not uniform over its width.
 The stress varies from a maximum in the web region to
progressively lower values at points farther away from
the web.
 In order to operate within the framework of the theory
of flexural, which assumes a uniform stress distribution
across the width of the section,
 IT IS NECESSARY TO DEFINE AN EFFECTIVE FLANGE
WIDTH
Flanged Beam/Section
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Flanged Beam
Cl 5.3.2.1 (EC2)
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How to determine 𝒃𝒆𝒇𝒇?
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Design Consideration
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Neutral Axis Lies in the Flange
Note: All the concrete on the tension side is assumed
ineffective in flexural computations, and the flanged
beam may just as well be treated as a rectangular section
having a width 𝑏𝑒𝑓𝑓.
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Neutral Axis Lies in the Flange
(Maximum Case)
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Example 6: Solution
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Neutral Axis Lies below the
Flange
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Flange
(Take moment @ steel reinforcement)
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Example 7: Solution
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Flange (M>𝑴𝒃𝒂𝒍 )
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Example 8: Solution
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Design Summary for Flanged
Beam
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End of Chapter 2
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L2 - Moment Design.pdf

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L2 - Moment Design.pdf