Question

Q1 A simply supported beam of length L = 10 m carries a uniformly distributed load w = of 10 kN/m, as shown in Figure Q1 (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 Q1 (b). Self-weight of the beam is neglected. 300 mm w = 10 kN/m 300 mm L/4 L/2 L/4 300 mm Figure Q1 (a) Figure Q1 (b) (a) Find the shear force V at X = 5 m. [5] 5 (b) Using the value of Vfrom (a), determine the maximum vertical shear stress and also the vertical shear stress in the web at the web/flange intersection. [20]

Answer 1

Given # Meglecting self weight Joomm W=10kN/m The 300mm B * * * 니다 니니 k 300mm L=lom # # Thicknen of all 3- rectangular membres १ lomm # Moment o inestia o I-fection 1300 X-320 300

Moment of Inertie of Rectangle I sect- MOJ about x = Moment of Inertia of small Rectangles at shown in fig below Removing shaded part from the Rectangle (320x360) bd² II 18 300 Rectangle 3 (2) (290)(300) (300) (320) 12 12 Tv ។ Ixx = 1.667x108 mm # Reaction (Support 10 kolm L=com mmm B RA 4₂ 44 RB 44 Rp U Etxcol (RA =RB EFx so, Rax=0 Petre = (10)(10) sokn As the is Symmetrical ORA=50 Beam IRA = 25kN /RB= 95KN

a) Shear force V at x 5m lotn/m min - * 9.5 RA= 95kN PR 25kn 5m x =sm um Shear force at V = SE 8 - (19)( 4/1) (10)(25) V = Sf = m = 25 - b) Maximum Vertical shear stres occull as shown 160 92 max FAG TE I b shear stren distribution b= 10mm M I 1.668 x 108 mm Ag + Ang ya AITAL V=0 from a) at section 5m

rovo Tmax H Shead stren distribution 4 vertical fuar heen at the led / flange in the wich intersention FAY T I bw b .bw (width of flange taken to asked to find shear sten at the in the key) (From a (at a motor) O at Favo NOTE: You alea either the shared while taking alla become easier can take area (a) Non shaded area make sure that calculation Conclusion O KN a @sm Tat web, in b) Tman : hleb flange intersection

Conclusion

a) V=0

b) max shear stress at section x=5m is 0

And vertical shear stress in the web at the web flange intersection is 0