Question

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The below wooden double overhanging beam is under a uniformly distributed load w. The wood is weak along the orientation of the grain (or wood cell fibres) that makes an angle of 30° with the horizontal (see figure). The maximum shear stress on a plane parallel to the grain that the wood can sustain is tmax = 5 MPa, and the maximum normal stress of wood is amax = 25 MPa. The Young modulus of this wood is E=15 GPa (a) Using w 18 kN/m, check if the beam is safe against failure & Determine the deflections at free ends and at the middle of the beam (b) Determine the value of w so that the maximum deflection of the beam will not exceed 2 mm AND the beam is safe against failure (c) If the uniformly distributed load w on the overhanging parts of the beam is removed (or w is applied over the 2-m span only), will the deflections calculated in question (a) increase or decrease. Explain with details (e.g. sketch) but no calculations. Sketch the bending moment and shear diagrams (d) If an additional concentrated force (vertical & downward direction) is applied in the middle of the beam (w is still applied over its entire length of the beam), will the deflections calculated in question (a) increase or decrease. Explain with details (e.g. sketch) but no calculations. Sketch the bending moment and shear diagrams W 200 mm 300 700 mm 700 mm 2000 mm 60 mm (A SSignmenot , AN M. Grmax 2 SMR? RA M=? N, 25 MA NA 2SMPa Zog= Eayles G=Gy) Rings Co DING Lll matee ecuer Assignmait It NA 200 6omm V Go x(L00[y + Ix 60 = (92S/ Ealyy 160-4 120 -Sn 20 2 26 2 Simple cedin) tanMattab er txce NG! COLUMN BUcteLi NG Sfrensth Gyveld A TE Ger Bucleling A- Eyreld hen C reld 2 CA-1 /COLUMN BuckeLiNG Bacleleny load Per Buchdeg Stoers Ger Por A A A A Cradius of gyhathan) Ger ehere A- 12 12 A 2 hh V12 Cer Xam ple CLUMN BUCiLING 31.4 x10 mm mt = T. 4.& x ib mmf L = 7m le 2 L = 14 m 4.9m 11 エユ_L 316, 23 teN Fer 316.23 TEIy 337.67 tN ?16.23 143.4にN。 2.2

Answer 1

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Strass eloment at A A A 30 22.0S mPa 200 Comprenive 2205 mPo Disect shao strers at ends = o in battom momort Stsios 22 o S is pinupof anca au oho sforjes bwil be les thon thi's Ol= 25Mfa Tmol eS.Fnat= in Autargyala Sechion . 25x1o X 60X200 2- .2SmPa < Taalo oz ST)Pa fen co safe

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0.7m B Aupepestio kB lee the pusad in beam doonwa Sin ta midoll span. Ag wi which tny i doonwad at mid we omove. Ov hay Ladiny RA Re Jerca Shaa C Im Gardtiny w-ra ms Memart wmld x tox (2m)x lox ( 2000)3 3HET X 3BY iSXla3x 2003 Wmid 6.25 man dou wa .575 kon ca inuease Proved

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