MODULE No 1 BENDING STRESS TIMBER DESIGN fb bending stress Sec0on modulus I moment of iner0a at the neutral axis f b f b MC I M S S 2bd 6 I 3bd 12 d 2 c dbd 42 2bd 8 Q I 3bd 12 SHEARING STRESS VQ Ib fv fv shearing stress V max ver0cal shear Q sta0cal moment of area Q Ay Q I moment of iner0a at neutral axis B width at cri0cal shear 1 For rectangular sec on f v 3 V 2 b d 2 For triangular sec on I bd 3 36 b 2 Q b b 2 d 3 d 2 2 bd 2 24 f v f v f v f v VQ Ib bdV 2 24 b bd 3 2 36 V 3 bd 2 2 V 3 A 2 f Q 4r 3 3 For circular cross secAon v VQ I b r4 I 4 Q Ay r2 2 2 r3 Q 3 b 2r V 2 3 r3 r4 4 2r v 4V 3 r2 v 4V 3 A Sample Problem v f f f 1 Problem A 100 mm x 300 mm rectangular beam carries a uniformly distributed load of W kN m over its enAre span The beam is freely supported at its ends If the max allowable bending stress is 8 27 MPa and simultaneously the max allowable shearing stress is 0 70 MPa 1 Which of the following gives the value of max verAcal shear 2 Which of the following gives the value of the span of the beam 3 Which of the following gives the value of W in kN m SoluAon f 1 Max verAcal shear v 3 V 2bd 3 V 0 70 2 100 300 V 14000N V 14 kN M 12 405x 106 N mm 12 405 kN m 2 Span of beam fb M 6 bd 2 27 8 6 M 300 100 2 M wL 2 8 12 405 WL 2 8 WL2 99 24 WL V 2 WL 28 WL2 99 24 WL 28 99 24 L 28 L 3 54 m 3 Value of W WL 28 28 3 54 W W 7 91 kN m 2 Problem A oor is supported by 75 mm x 200 mm wooden joists spaced at 400 mm on centers with an e ecAve span of 3 m The total oor load transmiRed to the joists is 5kPA Weight of wood of 6 3 kNm3 Ew 12 x 103 MPa 1 Which of the following gives the maximum bending stress 2 Which of the following gives the maximum shearing stress 3 Which of the following gives the maximum de ecAon of the joist SoluAon 1 Maximum bending stress Wt of wood 6 3 0075 0 2 1000 Wt of wood 945 N m Total wt of wood 3 W 94 5 5000 0 4 W 2094 5 N m WL 2 8 2094 3 5 8 mN 3 2356 x 2356 103 3 M 6 bd 2 6 2356 75 10 3 2 mmN 3 M M M M f b f b 200 Fb 4 71 MPa 2 Max shearing stress v f V V N V 3 bd 2 2094 3 5 2 75 3141 V 3 bd 2 3141 3 75 2 fv 0 31 MPa f f v v 75 200 y max 75 50 I I y max WL 5 4 EI 384 200 3 12 mm x 10 5 2094 384 6 4 ymax 3 68 mm 3 Max de ec on 3 5 4 1000 10 50 10 12 6 3 3 2 A CE Board May 2006 A Amber beam having a simple span of 4 m carries a total load including its own weight of 10 kN m lt has a width of 200 mm and a depth of 260 mm used dressed dimension by reducing its dimensions by 10 mm The wooden secAon is made up of 80 Apitong Use table on gure TM 6 1 Which of the following gives the max exural stress of the beam 2 Which of the following gives the max shearing stress of the beam 3 Which of the following gives the max de ecAon of the beam Solu on 1 Max exural stress of the beam Fb 16 5 MPa Ew 7310 MPa Fv 1 75 MPa M M wL 2 8 4 10 8 2 M 20 kN m f b f b M 6 bd 2 10 20 6 6 250 190 2 fb 10 105 MPa 16 5 MPa 2 Max shear stress 3 V fv 2 b d 10 4 V 2 V 20kN 3 20000 fv 2 190 250 fv 0 63 MPa 1 73 MPa 3 Max de ecAon of beam wL 5 4 EI 384 250 190 12 x 104 247 3 6 I I 5 384 10000 7310 18 43 mm 1000 4 4 3 10 4 247 6 2 B Problem A pontoon bridge is constructed of two longitudinal wood beams known as balks that span between adjacent pontoons and support the transverse oor beams which are called chesses Assume that uniform oor load of 8 kPa acts over the chesses and balks The chesses has a span of 2 m and the balks are simply supported with a span of 3 m Allowable bending stress of wood is 16 MPa If the balks have a square cross secAon compute the minimum required width SoluAon W 8 2 1 W 16 kN m M M M fw WL 4 8 4 3 16 8 mkN 18 M 6 bd 2 10 18 6 6 16 b 188 b 3 mm 9 Use b 190 mm 2 C Problem A oor system in a small building Consists of wood planks supported by 50 mm nominal width joists spaced at distance of U 40 m measured center to center The span length of each joists is 3 2 m The uniform oor load is 5 8 kPa which includes an allowable for the weight of oor system 1 Determine the total uniform load in kN m carried by the joists 2 Determine the required secAon modulus tor the jo1sts if the allowable bending stress is 9 30 MPa 3 Determine the depth of the joists SoluAon 1 Total uniform load in kN m carried by the joists W 5 8 0 4 1 W 2 32 kN m WL 2 8 2 3 32 2 2 M M 8 mkN 97 2 M MS f b 97 2 S 6 x 10 30 9 S 319 4 x 103 mm3 2 SecAon modulus required for joists WL 2 8 2 3 32 2 2 8 kN 97 2 M M M MS f b 97 2 S 6 x 10 30 9 S 319 4 x 103 mm3 3 Depth of joists S 2 bd 1 6 319 104 x 3 3 d 50 6 d 195 8 Use d 200 mm 2 D Problem A simple log bridge in a remote area consist of two parallel logs with plank across them The log has an …