Question

A rectangular concrete beam 250mm wide and 550mm deep is prestressed by means of 4 numbers of 12mm dia high tensile bars located at 200 mm from the soffit of the beam. if the effective stress in the wire is 700n/mm. what is the maximum bending moment that can be applied at the soffit of the beam

Answer 1

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

P

-

M

y +

Pe

y = 0

A I I

P = 700 ×

π

(7)2 × 16

4

= 431.0265 × 103N

∴

P

-

M

+

Pe

= 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