Question

A reinforced concrete beam of T-section is cast from N32 concrete. The beam has a flange width of 805mm, flange thickness 90mm, web width of 300mm and overall depth of 650mm. Two, N32 tensile rods with an effective cover of 46mm are located in web area, and four, N20 compressive rods with an effective cover of 25mm are located in the flange area. The center-to-center distance between the compressive rods is 225mm. The bending moment applied to the section is 475 kNm.  Using a modular ratio of 6.6, calculate the serviceable stresses in both the steel and the concrete.

Answer 1

805 mm Commo As 1650mm As 30omok Assuming Neutral knis in web. Dividing the section into afferent parts.

805 K K 300 (n-1) As se - 25 (650+90-46=694mm) 694-X - DAS As = 2 x 11 x 3 2 ² = 1608.5 mm As = 4x 1 x 20² = 1256.6 mm² Moment, M = 475kNm

Area x leveranm at compressive side - Areax lever arm at tensile side 90 (805-300) (x-45) +300 x 2 + (2 X 6.6-17 x 12 56.6. (X-25) - 6.6x (1608.5) (694x ) 4 5 4 502 - 20452 50+ 150m² +15330.52 2 282262 - - 2002 +15330.522-383263-736 7573.4 - 1066 x

15072+ 71397 X - 97954 04 = 0 ł = 11 mm Moment of Inertia 1 (300) (41193+ (805-300) (90)+ (805-300) (90) (11-45)? + (2x6:6-1) 1256.6x(111–25)2 +6,6X1608.5 (694-1002 for = 4087102 189 mm 4 Stresses Concrete fc = ma M X - 475X10 X 11 4087102189 = 12.90 N/mm² for Compression steel - f = 2n Mere-25) 2X6.6 x4 75x10 6 x (111-25) I or 4087102189 = 151.93 N/mm² Tension steel fo=n. M (694-x) - 6.6 x 47 5x 106 (694-11) Der 4087102189 = 447.19 N/mm²