REINFORCED
CONCRETE DESIGN
MECHANICAL PROPERTIES OF
REINFORCED CONCRETE
COMPRESSIVE STRENGTH
The compressive strength of concrete (f’c) is
determined by testing to failure 28 day old 6-in. by
12-in. concrete cylinders at a specified rate of
loading. Although concretes are available with 28-
day ultimate strengths from 2500 psi (17.5 Mpa) up
to as high as 10,000 or 12,000 psi., most of the
concrete used fall into 3000 (20.7 Mpa) to 7000 psi
range.
MODULUS OF ELASTICITY
Concrete has no clear-cut modulus of
elasticity. Its value varies with different
concrete strengths, concrete age, type of
loading and the characteristics of the
cement and aggregates.
Ec = 4700 √ f’c
Modulus of Elasticity is the ratio of the normal
stress to corresponding strain for tensile or
compressive stresses below the proportional limit of
the material.
Concrete has a modulus of elasticity which varies
with different concrete strength, concrete age, type
of loading and the proportions of cement and
aggregates.
Modulus of Elasticity Ec for concrete shall be permitted to be taken
as:
a) For values of wc between 1500 kg/m3and
2500 kg/m3
Modulus of Elasticity Ec for concrete shall be permitted to be taken as:
b) For normal weight concrete shall be permitted as
Ec = 4700 √ f’c
c) For normal weight concrete with f’c > 42 Mpa and up to 84 Mpa and for
lightweight concrete with f’c > 42 Mpa up to 62 Mpa
Different Definitions of the Modulus
a) Initial Modulus – is the slope of the stress-strain
diagram at the origin of the curve.
b) Tangent Modulus – is the slope of a tangent to the
curve at some point along the curve, for instance at
the 50% of the ultimate strength of concrete.
c) Secant Modulus – slope of a line drawn from the
origin to a point on the curve somewhere between
25% and 50% of its ultimate compressive strength.
d) Apparent Modulus or Long-term modulus – is
determined by using the stresses and strains
obtained after the load has been applied for a time.
POISSON’S RATIO
The ratio of the lateral expansion to the longitudinal
shortening. Its value varies from about 0.11 for the
higher- strength concretes to as high as 0.21 for the
weaker grade concretes, with average values of
about 0.16.
TENSILE STRENGTH
The tensile strength of concrete varies from about
10% to 15% of its compressive strength.
Two indirect test developed to measure
concrete tensile strength
1) The Modulus of Rupture Test
(Standard Beam Test)
A 100 mm x 100 mm in cross-section and 400 m
lone is loaded to failure by either a concentrated
load at midspan or by two loads applied at the
third points. The values of the modulus of rupture
can be computed by substituting experimental
values of moment into the standard beam equation
for the stress at the top and bottom surfaces.
fr = 0.62 λ √f’c, Modulus of Rupture (NSCP)
fr is then determined from the flexure formula
fr = Mcr C
I
Where: Mcr = cracking moment
Modulus of Rupture is the bending tensile stress
at which the concrete begins to crack
2. Split Cylinder Test
A cylinder is placed on its side in the testing
machine and a compressive load is applied
uniformly along the length of the cylinder, with
support supplied along the bottom for the cylinders
full length. The cylinder will split in half from end to
end when its tensile strength is reached. The tensile
strength at which the splitting occurs is referred to
as the split cylinder strength and can be calculated
with the following expression.
ft = _2P
πLD
Where: P = the maximum compressive force
L = the length of the cylinder
D = diameter of the cylinder
Shear Strength
It is extremely difficult in testing to obtain
pure shear failures unaffected by other
stresses. Tests of concrete shearing
strengths through the years have yielded
values all the way from 1/3 to 4/5 of the
ultimate compressive strengths.
Shrinkage
Shrinkage is the decrease in volume of concrete
during hardening and drying under constant
temperature. The magnitude of shrinkage depends
upon the composition of concrete. The hardened
cement paste shrinks but the aggregates does not
shrink, thus the larger the fraction of the total
volume of concrete that is made of hydrated cement
paste, the greater is the shrinkage.
Water-cement ratio affects the amount of shrinkage
because high water content reduces the volume of
concrete., thus reducing the restraint of the
shrinkage by the aggregates.
Types of Shrinkage
1) Drying Shrinkage- is due to the loss of a layer
of absorbed water from the surface of the gel
particles. This will occur as the moisture diffuses out
of concrete, and as a result, the exterior shrinks
more rapidly than the interior. Drying shrinkage is
the decrease in the volume of a concrete element
when it losses moisture by evaporation.
2) Carbonation Shrinkage – usually occurs in
carbon dioxide rich atmosphere, such as found in
parking garage. At higher and lower humidity, the
carbonation shrinkage decreases.
3) Plastic Shrinkage -occurs during the first few
hours after placing fresh concrete in the forms, In
such cases, moisture evaporates faster from the
concrete surface than it is placed by the bleed
water from the lower layers of the concrete
elements.
To minimize tensile cracking due to
shrinkage:
1. Cure the concrete well
2. Add reinforcements to limit the width of the crack
3. Use construction and expansion joints to conctrol
the location of cracks.
4. Minimize water content.
5. Limit the area or length of concrete poured at a
given time.
Creep of Unrestrained Concrete
Creep - is the slow deformation of a material over
considerable length of time of constant stress or
load.
Honeycomb – the absence of mortar between
aggregates which is developed when the concrete
contains insufficient mortar or when concrete is not
properly compacted in the forms.
Creep of Unrestrained Concrete
Brittle – a condition where members fail suddenly
without warning and with no time for measures to
be taken to prevent damage.
Hydration – the chemical reaction between cement
and water after the components of concrete have
been mixed together which produces significant
quantities of heat.
Behavior of Concrete Exposed to high
and low temperature
The modulus of elasticity of concrete decreases at
high temperature. During fire, high thermal
gradients occur as a result, the surface layers of
concrete expand and eventually crack or chip off
the cooler interior part of the concrete. The chipping
is aggravated if water from the fire hoses suddenly
cools the surface.
Modification factors λ as multiplier as √f’c
λ = 0.85 for sand-lightweight concrete
λ = 0.75 for all lightweight concrete
λ = 1.0 for normal weight concrete
λ = __f’ct__ < 1.0 for average
0.56 √f’c splitting tensile strength
of lightweight concrete
f’ct
