Question

all parts

A simply supported concrete beam is to be designed to span 8m. The beam is required to resist a dead load of 40 kN/m (which includes an allowance for self-weight) and an imposed load of 20 kN/m Calculate the ultimate design load that the beam will be required to resist and hence calculate the ultimate design moment. (10 Marks] b) Choose an appropriate depth and width of the beam. [5 marks] c) Calculate an appropriate amount of reinforcing steel to resist the ultimate moment [30 Marks] d) Comment on the appropriateness of your design in terms of its suitability for resisting bending moments [5 Marks] Note: The beam will use the following in its design fyk = 500 MPa fck=30 MPa Y = 1.15 Y = 1.5 Es = 205 000 MPa cover = 20mm Diameter of shear reinforcement = 8mm Page 2 of 5

Answer 1

Sol Giren Given :- tyk . 500MPa. tek = 30MPa Vc = 1.5 Y = 15 Es = 205 000 M Pa Cover = 20mm : Dia oj shear - ag mm. a) calculate ultimate delon load that the beam will be read. - to resist & hence calculate ultimate design moment. Dead load = 40 kn/m (self wt.) Live load = 20 kN/m Total udl = 40+20 = 60 kN/m. (Factored) ultimate design load = 60 kN/m * 1.5 = go kN/m The ultimate design moment will be = We M 908 - 720 kNm. : Mudimo @cenne C=T oo b) choose an appropriate depth & width of the beam. – The width of beam is generally taken anywhere between 230 mm to 300 mm Asuming , b {width of beam) = 250 mm - will require for Neutral axu " 0.36 fck.b. xu o calculation We have, Moment of Repútance = 0.36 feki b. Humax (d-0.42 Humax) = 0.36X 30x 250 x 0.46 d (d-0.42X0.46d) = 1242 08068) MoR = 100 2.045 de 720x106 = 1002.045 da 720x10C = 847.66 mm + cover 100 2.045 ã 850 847.66 +20 875 mm (MOR)

= 0'5x30x250x 275 500 46X 720x106 30x 250 *875 Ast = 2293.26 mm2] Area of steal required. - Check, it MoR of beam ở greater the design or acheal moment, - calculate tree Neutral axis, Bu = 0.8764 Ast - 0.87x500x 2293:26 0.36 fck b 6. Ku = 369.46 mm 7 0.36X30X250 Humax = 0464 0.46x875 = 402.5 mm under-rei Hence, nu Hence, safe numax, the beam is . . klidth of beam = 250mm Depth of beam c 875 mm co calculate appropriate amount of steel to resist moment. - The area of steel has been calculated in the above Section (b) . It is as followy: Asteel = 2293.26 mm. ove it can be represented as follows , < 250 Assumning 250 bass, No. of bars = 2293-26 1 x 25² D=815| = 4:67 * 5 bon ot 5-#2540 cross-section of beam.

2 d) Comment on appropriatness of design for suitability of resisting Bending moment → The beam ů having bending strength adequate to resist the bending moments → There is no dongee of failure due to shear forces. → The beam deflection ů under permissible lumits.