Introduction to Structural Reinforced Concrete in 1 Hour!

Concrete is made up of course and fine aggregate, cement, water, and possibly different types of admixtu

These materials are mixed together until a cement paste is developed in which most of the voids in the aggregate are filled , This produces a uniform dense concrete

After the materials are mixed, the plastic concrete is then placed in a mold and left to set, harden and develop adequate strength

Many factors influence the strength of concrete which may vary within limits of the same production method

This section of the course will focus on the main factors that affect the strength of concrete which include the water-cement ratio, the constituent properties, the mixing and curing methods, the  concrete age, loading scenarios, and the characteristics of the tested specimen

The water cement ratio is a very important factor affecting the strength of concrete .To achieve complete hydration for a  given amount of cement, a water cement ratio by weight equal to 0.25 is needed. If additives are not to be used, a water cement ratio of about 0.35 or higher is needed for the concrete to be reasonably workable.This ratio corresponds to 4 gallons of water per sack of cement. Using this ratio, a concrete strength of about 6000 PSI may be achieved. If the water cement ratio  is increased to 0.5 or 0.7, a concrete strength of about 5000 and 3000 psi respectively can be attained.

Concrete is a mixture of cement, Aggregate, and water. By increasing the cement content in the mix and by using well-graded aggregate, the strength of concrete can be increased. In order to attain the desired quality and strength of concrete, special  admixtures are usually added to the mix

The use of mechanical concrete mixers coupled with proper mixing time have led to positive effects on concrete strength. Vibrators can produce dense concrete with a minimum percentage of voids  A void ratio of only 5% can reduce the concrete strength by nearly 30%. Curing conditions such as moisture and temperature directly influence the hydration of cement. The longer the concrete remains in moist storage, the greater the strength. As far as temperature is concerned, if the curing temperature is higher than the initial temperature of casting, the subsequent 28 day strength of concrete is reached earlier than 28 days

As concrete ages, it gets stronger, while the hydration of cement continues for months. To find the strength of concrete, concrete cylinders and cubes are tested at 7 and 28 days. Practically speaking, it is assumed that concrete at 28 days is 1.5 times as strong as at 7 days: The extent varies between 1.3 and 1.7

For typical typical portland cement, the growth in strength with time, with respect to 28-day quality, may be taken as shown in the following table:

At 7 days, the strength of concrete is 67% of the 28 day strength.

At 14 days, the strength of concrete is 86% of the 28 day strength.

At 3 months, the strength of concrete is 17% greater than the 28 day strength.

At 6 months, the strength of concrete is 23% greater than the 28 day strength.

At 1 year, the strength of concrete is 27% greater than the 28 day strength.

At 2 years, the strength of concrete is 31% greater than the 28 day strength.

At 5 years, the strength of concrete is 35% greater than the 28 day strength.

The compressive strength of concrete is evaluated by loading a cylinder or cube to failure in a few minutes in compression. When placed under continuous loading for years, a 30% reduction in compressive strength occurs. When placed under continuous loading for 1 day, a 10% reduction in compressive strength occurs. When designing reinforced concrete members, factors such as sustained loads and Creep effects as well as dynamic and impact effects must be considered.

When checking the compressive strength of concrete, the most common sizes for  test specimens are either 6 in x12 in or 4 in x 8 in cylinders or 6in cubes.

If 2 cylinders are tested in compression and one is larger, the larger specimen gives a lower strength index.

This table shows the relative strength for different cylinder sizes as a percentage of the strength of the standard cylinder. The heights of all the cylinders are twice the diameter and the bigger the member, the lower the relative compressive strength.

In some instances, the testing specimen may not be a standard shape in which the height is twice the diameter.  The results from a nonstandard shape must be multiplied by a correction factor to compute the equivalent strength of the standard shape as shown in the “Strength Correction Factors” table. From this table, we can see that as the ratio of specimen height to diameter decreases, the strength correction factor also decreases because the relative strength increases.

And the table below shows the relative strengths of a cylinder vs cube specimen for different compressive strengths of concrete. From this table, we can see that as the compressive strength increases, the strength ratio of the cylinder to cube also increases.

In this video, we will discuss how concrete is tested and its failure modes.

The basic assumption when designing structural members is that the concrete resist compressive stresses and not tensile stresses. This means that the compressive strength is the defining characteristic of quality concrete and is denoted by f prime c. The remaining concrete strengths such as tensile, bending and shear are taken as a percentage of the compressive strength

Before testing, the specimens are moist cured. Then once the age of the concrete is 28 days, the specimens are tested. This consists of slowly applying a static compressive load until the specimen ruptures. Rupture can be caused by tensile stress, shearing stress, compressive stress, or a combination of all of these stresses.

The failure of the concrete can be explained with 3 different failure modes as shown in this figure.

The first mode of failure is shear and is resisted by both cohesion and internal friction.

The second mode is called splitting or columnar fracture in which the specimen separates into columnar pieces.

The third mode of failure is a combination of the first 2 modes, shearing plus splitting.

The stress strain relationship of both concrete and steel as well as the type of applied loading dictate the performance of a reinforced concrete member. Stress is equal to applied force divided by cross-sectional area and strain is equal to deformation divided by initial length. The stress-strain curve of concrete is obtained by recording the strain at different load points as the concrete cylinder is loaded to rupture

Here is a figure of stress-strain curves for concrete of varying strength.  They are composed of an initial relatively straight elastic portion. The maximum stress is reached at strain of about .002 and rupture takes place at a strain of approximately .003. Concrete with a compressive strength between 3 and 6 thousand psi is common, but high strength concrete with a strength greater than 6000 psi is gaining popularity as a building material for concrete structures

SInce concrete is a brittle material it cannot resist High tensile stresses. This is crucial especially when dealing with cracking, shearing, and torsional problem. High stress concentrations are to blame.

What’s happening is that when concrete is loaded in tension, certain portion of the member experience very high stress which cause microscopic cracks, yet other portions of the specimen experience low stress.

Generally speaking, the tensile strength of concrete varies from 7 to 11% of its compressive strength, and the average is 10%. There is an inverse relationship between compressive strength and relative tensile strength, meaning that the lower the compressive strength, the higher the relative tensile strength

We describe flexural strength of concrete in terms of the modulus of rupture, f sub r. The modulus of rupture is the maximum tensile stress in concrete during bending.  So when a beam bends, the lower half is in tension and the upper half is in compression.

By testing a plain concrete beam, F sub r is calculated using the flexural formula for elastic material which is Mc/I where M is the bending moment, c is the perpendicular distance from the neutral axis to the fiber of interest and I is the second moment of area about the neutral axis.

The modulus of rupture can range anywhere between 11 and 23% of the compressive strength

Reinforced concrete members rarely undergo pure shear because shear is typically coupled with normal forces. When pure shear occurs on an element, the element breaks transversely into 2 parts. Consequently, the concrete element must be able to resist the applied shear forces

Shear strength is taken as about 20 to 30% greater than the tensile strength or about 12% of the compressive strength.  

The modulus of elasticity is a measure of stiffness and is defined as the change of stress with respect to strain in the elastic range as the concrete is tested under compression.  Since concrete is as elasto-plastic material, the stress is not proportional to the strain and the relationship between the two parameters is a curved line.

The tangent modulus and the secant modulus are two attempts at defining the modulus of elasticity.

The tangent modulus of elasticity is the slope of the tangent to the stress-strain curve for a particular stress point. A specific form of this is the initial tangent modulus which is the slope of the tangent to the curve at the origin under elastic deformation. The problem is that this value is not very practical because it can’t be determined with accuracy.   Making things more challenging is the fact that the stress-to-total-strain ratio morphs into a changing nonlinear quantity as deformations become permanent.

The secant modulus is more practical than the tangent modulus.  It is denoted as the  slope of a line drawn from the origin to a particular point of stress on the stress-strain curve.  The point of stress that is usually used is the compressive strength divided by 2.

ACI Code 318-11 provides an easy way to to calculate the modulus of elasticity of normal and lightweight concrete with the secant modulus taken as half the specified concrete strength.

By assuming the unit weight is 145 lb/ft^3,  ACI Code 318-11 allows the use of the following formula to calculate the modulus of elasticity for normal-weight concrete

Here is a typical stress-strain curve of concrete

Line (a) is the initial tangent modulus, Line (b) is the tangent modulus at a certain stress, line (c) is the secant modulus also at a certain stress, and line (d) is the secant modulus at a stress equal to half of the compressive strength.

Poisson’s ratio is equal the transverse strain under axial stress divided by the longitudinal strain under axial stress within the elastic range.  For normal and lightweight concrete, this ratio is is between 0.15 and 0.2,

For isotropic elastic materials it is equal to 0.25. For simplification, 0.18 can be used as an average for concrete

Shear modulus is basically the modulus of elasticity in shear and it ranges from 40 to 60% of the modulus of elasticity in compression.