Department Building And Architectural Engineering.pptx

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1. Department Building And Architectural Engineering. Batch (22BAE). Subject: Mechanics Of Solids Subject Teacher: Engr. Abdul Qadeer Zar dari

2. Solid mechanics is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. What Is T he Mechanics O f S olids ?

3. Stress and strain are two of the most important concepts in materials science and engineering .  Stress refers to the force applied to a material per unit area , while strain is a deformation or change in the shape of the material that results from the applied forc e. What is the stress and strain?

4. Stress And Strain Formula’s Stress S train

5. Example:01

6. For Example: A stress on a rubber band produces larger strain (deformation) than the same stress on a steel band of the same dimensions because the elastic modulus for rubber is two orders of magnitude smaller than the elastic modulus for steel . The SI derived unit for stress is newtons per square metre, or pascals (1 pascal = 1 Pa = 1 N/m 2 ), and strain is unitless .  What is the stress and strain?

7. Uniaxial stress: It is defined as “The load divided by the cross-sectional area”. Unaxial Strain: It Is defined as the “Increase in length divided by the original length ”.  The stress is how much force you are applying, but the strain is the how much the material stretches. In a uniaxial measurement, the unloaded sides of the material contract inward. Unaxial State Of Stress And Strain

8. Lateral Strain:  lateral strain is also known as Transverse strain.  A Lateral Strain can be defined as the ratio of change in the width of a material to its original width . or Lateral Strain , is defined as  the ratio of the change in diameter of a circular bar of a material from its original diameter,due to deformation in the longitudinal direction. Types Of Strain

9. Example Of Lateral Strain

10. Volumetric strain is defined as the change in volume divided by the original volume, i.e., ΔV/V . Volumetric Strain

11. Poisson's ratio is a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression. Conversely, if the material is stretched rather than compressed, it usually tends to contract in the directions transverse to the direction of stretching. It is a common observation when a rubber band is stretched, it becomes noticeably thinner. Again, the Poisson ratio will be the ratio of relative contraction to relative expansion and will have the same value as above.  Poisson’s Ratio

12. Poisson’s Ratio

13. Poisson’s Ratio Formula Poisson's ratio = – Lateral strain / Longitudinal strain Range -1.0 to +0.5 Units Unitless quantity Scalar / Vector Scalar quantity

14. Poisson’s Ratio Of Some Materials.

15. When a brass rod of diameter 6 mm is subjected to a tension of 5 × 10 3  N, the diameter changes by 3.6 × 10 -4  cm. Calculate the longitudinal strain and Poisson’s ratio for brass given that Y for the bras Given :  Diameter of rod = D = 6 mm, Radius of wire = 6/2 = 3 mm = 3 × 10 -3  m, Load F = 5 × 10 3  N, Change in diameter = d = 3.6 × 10 -4  cm = 3.6 × 10 -6  m, Y for the brass is 9 × 10 10  N/m². To Find:  Longitudinal strain =? Poisson’s ratio = ?, s is 9 × 10 10  N/m². Example:02

16. Solution: Y = Longitudinal Stress /Longitudinal Strain ∴ Y = F / (A × Longitudinal Strain) ∴ Longitudinal Strain = F / (A × Y) ∴ Longitudinal Strain = F / ( π r² × Y) ∴ Longitudinal Strain = 5 × 10 3  / (3.142 × (3 × 10 -3 )² × 9 × 10 10 ) ∴ Longitudinal Strain = 5 × 10 3  / (3.142 × 9 × 10 -6  × 9 × 10 10 ) ∴ Longitudinal Strain = 1.96 × 10 -3 Continue

17. Now, Lateral strain = d /D =   (3.6 × 10 -6 )/ (6 × 10 -3 ) = 6 × 10 -4 Poisson’s ratio = Lateral strain / Longitudinal strain ∴ Poisson’s ratio = (6 × 10 -4 ) / (1.96 × 10 -3 ) = 0.31 Ans :  Longitudinal strain is 1.96 × 10 -3  and Poisson’s ratio is 0.31. Continue

18. Stress is the force acting per unit area. The force can be of any form. When the applied force is in the form of temperature the resultant stress is called Thermal stress. It is observed when an object expands or contracts due to a change in temperature. Thus, we can define Thermal stress as : “Stress caused due to the change in temperature”. It is measured using feet or metres. The effect of temperature on conductors is vital. The thermal conductors expand on heating and contract on cooling. What is Thermal Stress

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