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Exercise E5.2 A beam is to be made by gluing and screwing together four wooden planks of length 2 m, thickness 20 mm and widt
(a) Determine the second moment of area I for the three configurations shown in cross-section in the figure below. (b) Calcul
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120 4x20 x Ixx = (120) x180)3 = 5120000 mant 12 70 Ii - M.O.I about X-X С . 14 120 Jux = I, + I2 + Iz + In ](12018 (20)9_2890000 mm 1000 hmt Iz = Iy 120 20 70=10+60 Iz = I4 2120 x(2)3 + 120 x 20 x 702 12 - 2480004 I 2 6560000+248009)H 120 I, = I2 = (1271 20 = 2880000 mort Ty Ty 120Y&03947203204(85) = 7340000 mm 12. I= 2(Ist I3) - 2 (2880000 + 7340000) - 206 for wood = 13apa = 13x109 N =134103 N beso Jfo L=2 A=FL 48 EI ABEI L=2 Case I - 5120000 mm A, 100x1(213) mm 48 x 13x103 (N)Stiffnen Care I S-FE 48 EI - f 48 EI 8- 13 T: 5120000 48X13 103 4 5120000 (2000) 399.36 N = Cose I = 1-→ 29440000 F. 48x13410

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