SSC JE Civil Engineering 29-Oct-2020 Shift 1 Paper

Let ${\mathrm{\sigma }}_{\mathrm{c}}$ and ${\mathrm{\sigma }}_{\mathrm{T}}$ are the Compressive and tensile stresses developed in concrete at top and bottom fibre respectively due to given load ‘P’
Case 1:
Let an increasing the load, P (gradually), stresses in extreme, compression fibre reaches to its maximum permissible but in extreme tension fibres do not.
i.e.
${\mathrm{\sigma }}_{\mathrm{C}}=15\mathrm{MPa}$ (given) and
Now,
Using above equation (1)
$15=\frac{{\mathrm{\sigma }}_{\mathrm{T}}}{2}\Rightarrow {\mathrm{\sigma }}_{\mathrm{T}}=30\mathrm{MPa}>25\mathrm{MPa}$
Hence, our assumption is wrong.
Case 2:
Now, assume that stress in external bottom fibre tensile stress reduce and maximum permissible value but in extreme top fibre do not
i.e. ${\mathrm{\sigma }}_{\mathrm{T}}=25\mathrm{MPa},{\mathrm{\sigma }}_{\mathrm{c}}\le 15\mathrm{MPa}$
Now, from equation (1)
,
Hence.
⇒ compressive stress in extreme top fibre is 12.5 MPa which is less then its permissible value, when, extreme bottom fibre reaches to its maximum value.
Therefore, it can be concluded that failure of section will be due to stresses in extreme fibre reaching to maximum permissible tensile stresses, on increasing the load gradually.