A rectangular concrete beam 250 mm wide and 600 mm deep

A rectangular concrete beam 250 mm wide and 600 mm deep is pre-stressed by means of 16 high tensile wires, each of 7 mm diameter, located at 200 mm from the bottom face of the beam at a given section. If the effective pre-stress in the wires is 700 MPa, what is the maximum sagging bending moment (in kNm) (correct to 1-decimal place) due to live load that this section of the beam can with stand with out causing tensile stress at the bottom face of the beam? Neglect the effect of dead load of beam.

Since the tensile stress at bottom face of the beam is zero.

	P	-	M	y +	P_e	y = 0
	A		I		I

P = 700 ×	π	(7)² × 16
	4

= 431.0265 × 10³N

∴	P	-	M	+	P_e	= 0
	A		Z		Z

Since the prestressing force is located at 200 mm from the bottom face of the beam.
∴ Eccentricity = 300 – 200 = 100 mm

∴ =	413.0265 × 10³	-	M × 6
	250 × 600		250 × 600²

+	413.0265 × 10³ × 100	× 6 = 0
	250 × 600²

⇒ 2.8735 + 2.87351 = 6.66 × 10–8M
⇒ M = 86.205 kNm