Question

2 A simply supported beam of length L = 10 m carries both a uniformly distributed load w, of 10 kN/m and a non-uniformly distributed load with a maximum value of w2 =10 kN/m at its roller support, as shown in Figure Q2 (a). The beam is made from a I-section and the thickness for all the three rectangular members is of 10 mm. All other dimensions are illustrated in Figure 02 (b). Self-weight of the beam is neglected. 300 mm w1 = 10 kN/m w2 = 10 kN/m 300 mm L/2 L/2 300 mm Figure Q2 (a) Figure Q2 (b) [5] (a) Find the shear force V at X = 3 m. (b) Using the value of V from (a), determine the maximum vertical shear stress and also the vertical shear stress in the web at the web/flange intersection. [20]

Answer 1

EA lokN/m. S wilokN/m CS STO B. EG D CONY CONST 7 8 9 DEL AC MATRIX 4 VECTORY 5 6 Х STAT roPLUX 1 2 3 + Ray F 12225m 1625m KRB. e=10m. MA 20 = 1QR8 - 4x10x5(5+3+5) - 10x5x8.5 20 => TORB -333:33 20 RB = 33.33 KN @ Nat x=31 90kw/m Rod Ran Ranint 0 *10* Ans lokN/m. 3 second moment of inertia I 300X 320 290x300 12 I = 1.667x100mmy 12 V 2m. ARB V = 2X10 +5X5X10 – 33.33 IV=11.67KN Von Zmax -ra Ib 300mm 10mm T 7 Q = Aly, + A2Y₂ + A3 Y3 = 300 x10x5 + 300x10x 160 + 300x10x 315 300mm 10mm. q=1.44X106 mm3. Ilomm ba - lomm. 300 mm

Tmax = 11.67X103 x 1.440106 1.667x108x10 Tmax 210.08mpa. @ smm 150mm N Area of flange A = 300x10 ly = 155mm, A = 3000mm 2 y = 155mm a distance of centre of Area from N.A. I - 1.667x lodmm4 balomm. T=VAY 11.67X103 x 3000x155 Ib 1,667x108 x 10 T - 3.255 mpa,