Descripción: Course class notes of Reinforced Concrete
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10/20/2016
Working Stress Analysis for Concrete Beams | Reinforced Concrete Design by WSD Method
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Working Stress Analysis for Concrete Beams
Consider a relatively long simply supported beam shown below. Assume the load wo to be increasing progressively until the beam fails. The beam will go into the following three stages: 1. Uncrack Concrete Stage – at this stage, the gross section of the concrete will resist the bending which means that the beam will behave like a solid beam made entirely of concrete. 2. Crack Concrete Stage – Elastic Stress range 3. Ultimate Stress Stage – Beam Failure
Concrete Beam Crack Stages At section 1: Uncrack stage a. Actual moment, M < Cracking moment, Mcr b. No cracking occur c. The gross section resists bending d. The tensile stress of concrete is below rupture At Section 2: Boundary between crack and uncrack stages a. Actual moment, M = Cracking moment, Mcr b. Crack begins to form c. The gross section resists bending http://cereference.com/book/reinforcedconcretedesignwsd/workingstressanalysisbeams
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Working Stress Analysis for Concrete Beams | Reinforced Concrete Design by WSD Method
d. The tensile stress of concrete reached the rupture point At Section 3: Crack concrete stage a. Actual moment, M > Cracking moment, Mcr b. Elastic stress stage c. Cracks developed at the tension fiber of the beam and spreads quickly to the neutral axis d. The tensile stress of concrete is higher than the rupture strength e. Ultimate stress stage can occur at failure
Working Stress Analysis – Uncracked Stage The beam will behave elastically and remains uncracked. The tensile stress of concrete is below rupture.
Cracking Moment NSCP 2010, Section 409.6.2.3 Modulus of rupture of concrete, fr Cracking moment, Mcr
=
fr Ig
− − ′ = 0.7√ fc MPa
yt
Where Ig = Moment of inertia of the gross section neglecting reinforcement yt
= distance from centroid of gross section to extreme tension fiber
Working Stress Analysis – Cracked Stage http://cereference.com/book/reinforcedconcretedesignwsd/workingstressanalysisbeams
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Working Stress Analysis for Concrete Beams | Reinforced Concrete Design by WSD Method
General Requirement Actual Stresses ≤ Allowable Stresses Internal Couple Method Static equilibrium of internal forces
Factor k: fc
k =
fc +
fs n
Factor j: j = 1
1 3
k
Moment resistance coefficient: R =
1 2
fc kj
Moment capacity: Use the smallest of the two Mc = C jd =
1 2
fc kj bd
2
= Rbd
2
Ms = T jd = As fs jd
Transformed Section Method Convert steel area to equivalent concrete area by multiplying As with modular ratio, n.
Working Stress Analysis for Concrete Beams | Reinforced Concrete Design by WSD Method
Location of the neutral axis from extreme compression fiber Singly reinforced: 12 bx2
= nAs (d − x)
Doubly reinforced: 2 bx2 1
′
′
+ (2n − 1)As (x − d ) = nAs (d − x)
Cracked section moment of inertia (INA = I cr ) Singly reinforced: IN A
bx
3 2
=
+ nAs (d − x )
3
Doubly reinforced: IN A
bx = 3
3 ′
′
2
+ (2n − 1)As (x − d )
2
+ nAs (d − x )
Actual stresses (calculate using Flexure Formula) Concrete Mx fc =
IN A
Tension steel fs
M (d − x) =
n
IN A
Compression steel for doubly reinforced ′
′
fs 2n
M (x − d ) = IN A
Tags: Cracking Moment
Crack Stage of Concrete
Uncracked Stage
Example 01: Required steel area of reinforced concrete Example 02: Total compressive force in conrete Example 03: Moment capacity of a concrete beam Example 04: Compressive Force in Concrete TBeam Example 05: Stresses of Steel and Concrete in Doubly Reinforced Beam ‹ Reinforced Concrete Design by WSD Method
Example 01: Required steel area of reinforced concrete › 4/7
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Working Stress Analysis for Concrete Beams | Reinforced Concrete Design by WSD Method
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Reinforced Concrete Design by WSD Method Working Stress Analysis for Concrete Beams Example 01: Required steel area of reinforced concrete Example 02: Total compressive force in conrete Example 03: Moment capacity of a concrete beam Example 04: Compressive Force in Concrete TBeam Example 05: Stresses of Steel and Concrete in Doubly Reinforced Beam Design of Concrete Beam Reinforcement using WSD Method
