BCV108 STRENGTH OF MATERIALS - Lecture 3: Strain and Strain Energy

Flashcards covering linear and lateral strain, Poisson's ratio definitions and values for materials, and strain energy formulas for normal and shear stresses based on the BCV108 STRENGTH OF MATERIALS Lecture 3.

__________ is defined as the ratio of axial deformation to the original length, representing deformation in the direction of the applied load.

Linear (direct or longitudinal) strain

The strain occurring at right angles to the direction of the applied load is known as __________.

Lateral strain

Poisson's ratio ($\upsilon$) is mathematically defined as the ratio of __________ to __________.

$$\frac{\text{Lateral strain}}{\text{Longitudinal strain}}$$

Poisson's ratio is named after the French mathematician and physicist __________, who lived from 1781 to 1840.

Baron Siméon Denis Poisson

The values for Poisson's ratio typically range between __________ and __________.

$0.0$ and $0.5$

In the design of concrete structures, Poisson’s ratio is usually taken as approximately __________, while for steel structures, it is approximately __________.

$0.2$ and $0.3$

The energy absorbed and stored in a strained body, which is equal to the work done by the applied load, is called __________.

Strain energy

The formula for strain energy ($U_G$) stored in a body due to a gradually applied load is __________.

$$U_G = \frac{\sigma^2}{2E} V$$

When a load is applied suddenly, the maximum instantaneous stress induced ($\sigma_S$) is __________ the stress induced by a gradually applied load ($\sigma_G$).

$2$ times

The measure of rigidity of a body, defined as the ratio of shear stress ($\tau$) to shear strain ($\gamma$), is called the __________.

Shear Modulus Of Rigidity

The strain energy ($U$) stored in a block due to shear stress ($\tau$) is calculated using the formula __________.

$$U = \frac{\tau^2}{2G} V$$

For a bar consisting of three lengths, the total extension ($\Delta L$) is calculated by the formula __________.

$$\Delta L = \frac{F}{E} \left( \frac{L_1}{A_1} + \frac{L_2}{A_2} + \frac{L_3}{A_3} \right)$$

In structural analysis, the __________ criterion is used to predict fracture loads of two thin plates subjected to large elastoplastic deformation.

strain energy density

According to the Poisson effect, a material like rubber will __________ in cross-sectional area and __________ in length when stretched under a tensile load.

reduce and increase

To determine the stress induced in a plinth by a full water tank, the total load is calculated as the sum of the __________ and the weight of the water.

self-weight of tank