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Formulas in Concrete

This document provides descriptions and formulas for concrete design. It discusses working stress design which allows elements to remain within the elastic limit. Key aspects covered include: - Modulus of elasticity formulas for concrete and steel - Allowable stresses for concrete and steel - Internal couple method for singly supported beams with one layer of reinforcement - Transformed section method for singly supported beams with one layer of reinforcement

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Joshua Inciong
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119 views2 pages

Formulas in Concrete

This document provides descriptions and formulas for concrete design. It discusses working stress design which allows elements to remain within the elastic limit. Key aspects covered include: - Modulus of elasticity formulas for concrete and steel - Allowable stresses for concrete and steel - Internal couple method for singly supported beams with one layer of reinforcement - Transformed section method for singly supported beams with one layer of reinforcement

Uploaded by

Joshua Inciong
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Concrete Design I

Symbol Description

f’c Specified compressive strength of


6. Modular Ratio:
concrete, MPa

fc Allowable compressive stress of


concrete

= 0.45 f’c Working Stress Design

Ec Modulus of Elasticity of Concrete A design method for reinforced concrete


structural elements by allowing the elements be
Es Modulus of Elasticity of Steel
only stressed within the elastic limit.

Assumptions:
Formula:
1. Plane section remains plane after
1. Modulus of Elasticity of concrete: bending, i.e., the variation in strain is
linear across the depth of the member.
2. Stress is proportional to strain
3. Concrete does not take tension
4. Perfect bond exist between steel and
concrete such that no slippage occurs

2. Modulus of Elasticity of Steel:

Internal Couple Method (Singly Supported,


One Layer)

3. Tensile Strength of Concrete: Formula:

a. Moment Capacity of Concrete:


4. Allowable Stress in steel:
a. Grade 275 – fs= 140 MPa b. Moment Capacity of Steel:
b. Grade 415 or higher – fs = 170
MPa’ c. ; Balanced condition:
5. Modulus of Elasticity:
Sabay mag fail concrete and
a. For concrete:
steel so: Mc = Ms
b. For steel:
d. ; Rectangular section,
singly reinforced, single layer

Where:
 d = effective depth to the
centroid of all the
reinforcement
 f’c = allowable stress in
concrete
b. Moment of Inertia (taken from
 fc = 0.45 f’c
 fs = allowable stress in steel Neutral axis)
 b = width of section
 As = total area of tension steel

c. Flexure Formula:
a. Concrete:

b. Steel:

Transformed Section Method (Singly


Supported, One Layer)

Formula:

a. Moment Area below = Moment

Area above the neutral axis of


the section

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