A simply supported beam of overall depth 150 mm has neutral axis at 50 mm from extreme top fibre. Permissible flexural stresses in extreme compression and extreme tension fibre are restricted to 15 MPa and 25 MPa respectively. If the load on the beam is increased gradually, then:

EXPLANATION:Let σc and σT are the Compressive and tensile STRESSES developed in concrete at top and bottom fibre respectively due to given load ‘P’Since, stress DISTRIBUTION is Linear\(\frac{{{σ _c}}}{{50}} = \frac{{{σ _T}}}{{100}}\)⇒ \({σ _c} = \frac{{{σ _T}}}{2}\) ---(1)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.σC = 15 MPa (given) and σt < 25 MPaNow,Using above equation (1)15 = σT/2 ⇒ σT = 30 MPa > 25 MPaHence, 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 noti.e. σT = 25 MPa, σc ≤ 15 MPaNow, from equation (1)σC = 25/2 = 12.5 MPa < 15 MPa, 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.