Question

Figure 2a shows a composite beam made by placing three steel plates inside a wooden
section.
(a) Determine the maximum bending stress developed in the wooden section and steel plate
if the beam is subjected to allowable bending moment, M of 20 kN.m. Given that the
Modulus of Elasticity of wood is 13.1 GPa and steel is 200 GPa.
[14 Marks]
Figure 2a: Composite beam
(b) Figure 2b shows another beam without steel plates. Suggest the maximum bending
stress for the beam if the allowable bending moment is 20 kN.m.
[6 Marks]
Figure 2b: Wooden beam without steel plates
MEMB243 / MEMB2024, Interim S

Figure 2a shows a composite beam made by placing three steel plates inside a wooden section (a) Determine the maximum bending stress developed in the wooden section and steel plate if the beam is subjected to allowable bending moment, M of 20 kN.m. Given that the Modulus of Elasticity of wood is 13.1 GPa and steel is 200 GPa. [14 Marks) 24 mm 24 mm 24 mm It 111 300 mm x 100 mm 100 mm Figure 2a: Composite beam (b) Figure 2b shows another beam without steel plates. Suggest the maximum bending stress for the beam if the allowable bending moment is 20 kN.m. [6 Marks) 272 mm 300 mm Figure 2b: Wooden beam without steel plates

Answer 1

а. Given a composite beam of wood and steed. Anoodes to find wood & steel too we need to convest the beams into equivalent beaus in wood & sted section the maximum bending stress in 24 24 29. wood section equivalent when we convest this into deplace Steel with wood mx24 Es Ew we deplan with a thickness / where m= - 100 200 13.1 15.26. lor The wood equivalent beam is as shown MX 24 mx24 | mx 224, mx24 366.24 300 mm + oo My 1 100 366.24 (or 366.24 366.24 + 1298.72 mm 626M bd2 Maximum Bending stoess in wood 6xM bd 2 3 3 6 x 20x10x10 Nam ? 1.026 MPa 2 1298.72 X 3000 Similarly converting this into equivalent steel beam Ew Es ma 2 13.1 200 2 0.6655 6.55 The equivalent sted beams is 300 mm 24 85.1 mm & max steel 2 68M bd2 6x20x106 85.1 X 3002 15.66 MPa 6 620X10 2 Maximum be bending stressa EM bd² 4.901 MPa 272 X 300