The point loads are placed at the fixed positions shown in the figure and they are live loads. A k a b a b dn = 1₂ Icr = M B Aso Cross section Asc Ast N.A. Ast Stress profile (concrete) Cross section before cracking Q2) Now, the live load increases gradually and the moment at the critical section just exceeds the cracking moment (Mcr), but the compressive section of the concrete is still under the linear elastic region. Please be reminded that in the flexural design, the crack of the concrete section starts where the tensile stress reaches the tensile strength. It is assumed that the cracks then propagate rapidly up to the entire tension section (up to the neutral axis) and this cracked concrete section cannot resist the tension. It should be noted that in reality, concrete sections between the primary cracks can still resist some tensile stresses as shown in the figure, which should be considered in the displacement design. However, in flexure design, we design the critical section where the largest moment occurs and thus it is reasonable to have such a primary crack in this critical section. 2.1 Find the new neutral axis in the cracked section under the elastic region on the compressive section and also find the cracked second moment of areas (Icr). The transformed area method (dn = Σyi A₁/A₂) is still valid. However, we may need to solve the quadratic equation for calculating the neutral axis distance from the top surface. J 1₂ secondary crack W mm C (centre) f' = 38 Mpa f'ctf = 3.5 MPa fsy = 500 MPa E, = 200 GPa E = 28600 MPa 10⁹ mm¹ a D + b a Neutral axis primary cracks 4₂ A N.A → cracks Ast Cross section just after cracking $ Stress profile (concrete) M → -concrete in tension O Variables 1₁2.5 m 1₂3m a b с ASC Ast 55 mm 600 mm 400 mm 620 mm² 3200 mm² E