Question

A wooden beam with rectangular cross-section is supported by means of a pinned joint and a roller as shown. A static force is applied to the beam as shown. Assume that the pin joint and point A are located on the centreline of the beam. If grains of wood in the beam at point A make an angle of 25° with the horizontal as shown, determine the normal and shear stress that act perpendicular and parallel to the grains due to the loading. Sketch this on a 2D stress-element. 15 kN y -3 m 2 m 6 m 30° А. 400 mm ►x 25° 200 mm 200 mm (Diagram is not to scale; Point A is located on the neutral axis) Total 15 marks

Answer 1

wo vusi WE 2m * aho wwooh 8 Caluhoon hold By Ify 20 (1) PBX 1500szo' 13 KM och 3 hout hy 5 RAY +PBY Hous-t=,ocuISSI Taking & IMA, Ry X!! = 4:5X5 Roy = 3.499 kal 2.5-3.409 = 4.09096 Live Sheon force on Dragram 4.0909kn! C AI A 3.40KN Berding Moment Dia gramt Mmax Mmar PAT sx sx boboch = had to A, B mar = 20.4545 kilom A MA Part *3 = 12.2727 kN.m.

Mormal Force Dra agram (4) Temsile, el comprensive 3.4oq kul + A B A lies at neutral anis. so ooo VAY t= at neutral anys 2= 7 max V mid imax 2. = 115* 4,0909 mo? = 0.0767 MPa 2007 400 3. 13x103 RBX normal 0.1625 MPa A 200X Yoo on 525 (20 20 representation) The normal sctrey on the grain cnclined at 25. on wore +22 sino caso = 0.1625 ACCOS(25:))? + 2x0.0762 x sinds x cosas 0+ 2MP4 The shear stress on the grain cinslined at 250 is ž= -On Sino.cos + Z00520. = -0.1625 tsin 28.00525 +0.0767 X COSOU'). -0.013 MPa