#### Building Materials used in the Construction Industry

#### Young’s Modulus and Tensile Testing. Illustrate your essay with specific examples.

##### Introduction

The design of various construction structures such as buildings, dams, bridges, towers etc. is primarily determined by two major parameters, namely, the strength of the structure and the stiffness of the structure.

While Stress is related to the strength of a material, the Modulus of elasticitydescribes the inherent stiffness of a material.

##### 1.1 History

Although builder since the medieval age already had concepts for building structures, Italian polymath Leonardo da Vinci (1452:1519) was the first person who performed scientific experiments to determine the strength of materials. Galileo followed by publishing the first formal text ever on the subject of materials entitled “Dialogues concerning two new sciences” in 1638; when he was under arrest for having antagonized the Vatican by proposing that the Earth went around the Sun and not the reverse.

Although, Galileo’s dialogues was not very accurate and correct and the basic laws of physics had not been discovered then; Galileo’s thoughts did get people thinking.

Robert Hooke was very much interest in this subject and he probed further examining the ways in which materials responded to forces, and subsequently came up with Hooke’s law,

force = stiffness * compression

During his experimentation he applied it to a spring ; however subsequently it was learnt that the law also applied to other structural elements made of material like hard metals, stone, glass etc.

It, however, did not hold true for flexible materials like rubber or tendon, which stretch easily up to a limit but then yield diminishing returns.

Hooke’s work was the first to at least imply the notions of “stress” and “strain”. Stress is a force applied to a structural element. Such forces include:

Stress is defined as the force per unit of area, or what is simply known as “pressure”. The formal metric unit of pressure is the “pascal (pa)”, which is a newton per square meter, named after the great French mathematician and physicist Blaise Pascal (1623:1662). Since a pascal is a somewhat small unit, it is often expressed in terms of “kilopascals (kpa)” — thousands of pascals — or “megapascals (Mpa)” — megapascals.

##### Types of forces:

A brief description of the forces and their nature is as given below:

Strain is phenomenon of “lengthening” experienced by a structural element when it is under stress, given in a simple proportion.

Elasticity is defined as the phenomenon by which a material returns to its original shape after removing a stress.

Although Hooke proposed this concept, Thomas Young was the first person to publish a paper in 1807 on the same, in which he defined the concept of “elastic modulus” or “Young’s modulus”, developed the idea further. In modern terms, this is the ratio of stress of a particular material to its strain:

Materials that stretch easily possess a low elastic modulus value (rubber has an elastic modulus of 7). Stiffer materials possess higher values of elastic modulus (consider examples of stiffer materials as shown below).

Using the equation above, Hooke’s law can be rephrased as follows:

When the incremental loading is increased beyond the “Yield Stress Point or elastic limit”, the structural member will either deform permanently or will break.

When the material responds in a non-linear fashion with lots of deformation with little applied force beyond the yield stress point, it is called a ductile material. An example for ductile material is

Metal beams. It is an attractive material for building material as it bends but doesn’t break while making it. In natural phenomena, such as a small earthquake occurs and the stresses are in the metal’s elastic region, the building structure will survive with no major damage. The building structure would get damaged if the stress goes beyond the elastic region; however it would still not fall. By virtue of its ductile nature, it would be permanently changed in this condition thus enabling easy identification of the location of the structural damage.

Materials, which fail beyond the yield stress point, are called brittle material. Glass is an example of brittle material.

Metals are usually strong in both compression and tension however stone is very strong in compression but is weak in tension. Wood can be split easily by shear forces applied along the line of its grain, but will resist larger shear forces applied at a right angle to its grain.

##### 2. Theory

##### 2.1 Young’s Modulus

Young’s modulus can be defined as

- A measure of elasticity (or conversely, stiffness) of a solid substance such as a metal, polymer, ceramic, or glass or a measure of the material’s resistance to deformation.
- The ratio of stress vs. strain or E=stress/strain within a material’s elastic limit. Beyond the elastic limit, other forces come into play.

It is independent of the shape and is constant for a material. Denoted by the symbol “E”, its units are force / area i.e., PSI or N/m2

##### 2.2 Moment of Inertia

Moment of inertia is defined as a measure of a material’s resistance to bending or buckling. It is dependent on the cross-sectional area of the specimen under observation.

Denoted by the symbol ‘I’, its units are in length4 (in4 or mm4).

##### 2.3 Calculation of Modulus of Elasticity using Moment of Inertia

Young’s modulus is also the linear portion of a stress-strain curve when measuring the tensile strength of a material.

Consider the example below for calculation of Young’s Modulus for a sample possessing length 50mm and a diameter of 5mm:

As the unit for Young’s Modulus is N/m2, all units need to be converted according and then the readings are to be plotted on a graph of force against deflection. The slope of the line of best fit

The value is nearest to Lead with a Young Modulus value of 16 GPA therefore there is a probability of the wire being composed of lead.

##### 2.4 Structural design & Young’s Modulus

Structural design is primarily based on the concept of balance of stresses. If the stresses imposed on a structural element exceed the strength of the element, it will collapse. The stresses are set up due to the “loads” on these structural elements. These loads on a structure comprise of the “dead load”(set up by the weight of the structure) and the “live load”(set up by the people, furnishings, equipment, and materials contained in the structure). These loads are termed as “static loads” because they don’t change, or don’t change much, over time.

“Hidden” are those loads that are set up by the expansion or contraction of structural elements due to changes in temperature, or by unequal settling of the building’s foundations. Structures may also be subjected to rapidly changing “dynamic” loads, such as those caused by winds and earthquakes. Dynamic loads can be particularly treacherous since they are somewhat unpredictable.

##### 3. Discussion

Structures can be divided into two classes: compressive structures, in which the structural elements are stacked on top of each other; and tensile or “suspension” structures, in which the structural elements are suspended from supports.

Consider the construction of a bridge as an example to understand Young’s Modulus for the building materials and different types of loads that have to be carried which in turn influences the design of the structure. Wood tongue depressors (6″), Glue guns and glue sticks and String are the basic building materials for the bridge. The Young’s Modulus for wood is 11,000 Mpa. As stated earlier, wood can be split easily by shear forces applied along the line of its grain, but will resist larger shear forces applied at a right angle to its grain. Various structural designs such as beam, arch, suspension, truss etc. can be used for the bridge design.

In case of the beam, we may deploy various methods such as using an appropriate cross section design (moment of inertia), using stronger materials (elastic modulus), decreasing overall length (deflections) or using reinforcement to strengthen members in bending.

If an arch is used, it puts its members in compression and therefore requires horizontal support at its abutments.

On the other hand, if a suspension is used, it puts its members in tension. It however carries weight to the top of the towers and is good for long spans.

A Truss loads its members with both tension and compression. The members at pinned at its joints (Moment=0). The triangles provide stability and strength. The top members would be in compression while the bottom members would be in tension.

Thus the design of the bridge can be improved by incorporating a truss structure (triangles), designing a 3-D structure, using short members in compression, using string for tension members, avoiding overloading joints, strengthening base supports and load point and maximizing moment of inertia of cross-section.