Question

PROBLEM: A thin-walled cantilever beam of unsymmetrical cross-section is subjected to a uniform distributed load was shown in the figure below. The wall thickness t can be assumed to be very small in comparison with hin calculating the sectional properties. Determine the stress distribution on the cross section and the position of the neutral axis. Find the deflection of the beam at the cross section. Use:w=0.8N/mm: L = 1500 mm; h = 80 mm: t= 2 mm: E = 70 kN/mm2; z = Group_ID*100 mm.

Z = 13*100mm

Answer 1

Given that,

w = 0.8 N/ mm

L = 1500 mm

h = 80 mm

E = 70 k N/ mm ²

<sup>ASW L + Herre, e Tx=3x hxt² + 2x the 12 12 Ix = Box 2% Cey Ix = 80 +170, 666 Ix=1707.47 mm" wwimmi Cross section wiosnimm 2 1200 mm 2 =1500 mm

=) The caoss-section is at By Here, shead force at AB SAB = wxx 38/2 = 1100mm- 0.8 X1100 158 = 8800] Bending moment at B MB = w x 2 MBP = too - 30sx 12 x 104 1 MB= 2184 x 103 Nmm =) Nutral axis-tech (centroid of t, .+12.) Nutralaxis 4 Ut,"Ab, Aa, Ac Adi Ae Area of section A, B,C,D,E srespectively.

Then neutral axis y y Autat AbY TAYTAĞ Aatab+Actad * 2X40 X 80+ 2x 40x60+2 X 40 X 40+2X40X20 (wxno)XMO y = 80 +60+1+0+20 TY = 50mm from bottom .. Neutral axes rige at somm re. 30 mm from top. -) stress distribution: Stress due to Bending : I at. Y = heutral. axis (y=0), 1 0 06 top od Y= 30 mm ob= -4841 x 103 +(-30) 170747 626 too 85 N Imm2 /

-bbottom y =50mm bbo Hom = - To both 48mx 103 x 50 7 1707417 -bbottom = 2.27 N/mm2. Bending stones distribution:- To hap Neutsal axis Somm Tolbottom</sup>