2. Your client wants to install a heavy safe on the second floor of a building. As the structural engineer, you decide to reinforce the existing timber bearer by specifying a parallel flange channel (PFC) screw fixed to the bearer in the configuration shown (Fig. 2 overleaf). The beam shear X of the composite beam has already been calculated for you. Refer to tables and the appendix for timber bearer sizes and PFC details. NOTE: The modulus of elasticity of spotted gum is approximately 20GPa compared to 200GPa for steel. a. The timber beam consists of multiple laminations of 45mm spotted gum. Determine the longitudinal shear stress t at the interface between the two lowermost laminations of the bearer (i.e., 45mm above the bottom of the bearer) if the floor was loaded up before the PFC could be installed? (15%) You specify to the builder that the PFC must be fixed to the timber beam with coach screws at 300mm spacings. Allowing a factor of safety of 2, what is the minimum required shear capacity for the coach screws? (20%) X6 kN TIMBER BEARER X7 mm x Xg mm Floor Joists X, PFC Figure 2 SPECIAL NOTE: When calculating the moments of area (both I and Q) for this composite beam, you must transform the composite section to account for the difference in E values. If you are doing an ‘all steel’ transformation, you will need to multiply the width of the timber beam by the ratio of the two E values as illustrated in Fig. 3 below. ber Ewood.be Esteetbo + (L) Original Section (R) All Steel Transformed Section Figure 3 Parallel Flange Channels About x-axis Abouty-axis Table 19 Parallel Flange Channels – Dimensions and Properties Designation Mass Depth Flange WebRoot Depth per of – Thick- Radius Bet- metre Sec Width Thickness woend ( tion ness Flanges Warp Torsion Cont Designation Gross Coordi- Coordi- Area of nate of nate of w) Cross- Con- Shear Section froid Centre stant Con- siant 380 40.1 300 100 90 90 380 PFC 300 PFC 250 PFC 230 PFC 200 PFC 180 PFC 150 PFC 125 PEC 100 PFC 75 PEC 25.1 22.9 20.9 17.7 11.9 8.33 5.92 230 200 180 150 125 100 75 75 75 75 65 50 40 175 16.0 15.0 12.0 120 11.0 95 75 6.7 .1 100 14. 0 8.0 14.0 8.0 12.0 6.5 12.0 60 120 6.0 12.0 6.0 10.0 4.7 8.0 4.2 8.0 3.8 8.0 mm mmmm 10mm 10mm10mm mm 108mm 10mm 10mm 345 345 5.1470310 27556712798946147 648 894 236 268 33. 5 5.13 5110 272 56. 1 72.4 483 564 119 4.04 64.4 148 220 275 5.47 4520286 585 45.1 361 421 99.9 3.64 59.3 127 206 31.7 5.71 3200 226 46.7 268 233 271 91.4 1.76 33.6 77.8 176 293 5.75 2920 244 505 1 9.1 191 221 80.9 1.65 32.7 678 158 26 3 627 2660 245 50.3 14.1 157 182 72.9 1.51 29.9 51.5 131 218 726 2250 249 51.0 8.34 11112960. 8 1.29 25.7 51.6 110 234 8.04 1520 21 8 45.0 3.97 63.5 73.0 51.1 0.658 15 2 30.2 866 206 6.84 1060 16.7 33.9 1.74 34. 7 40. 3 40.4 0.267 8.01 16,0 628 165 5.94 754 3.7 27.2 0.683 18.2 21.4 30.1 0.120 4.56 8.71 10mm3 161 117 107 61.0 58.9 53.8 46.0 272 14.4 820 mm 10mm 30.4 472 28.1 200 28.4 238 23.5 103 23.8 101 23. 8 8 1.4 23.9 54.9 20.8 23.1 15.9 132 12.6 .13 10mm 151 58.2 35.9 15.0 106 7.82 4.59 1.64 0424 0.106 380 PFC 300 PEC 250 PEC 230 PFC 200 PFC 180 PEC 150 PEC 125 PFC 100 PFC 75 PEC 6 Table 20 Parallel Flange Channels – Properties for Assessing Section Capacity Designation Yield Stress Form A bout x-axis About y-axis Factor Flange Web Load A Load B Yield Stress Form Factor About x-axis Designation About y-axis Load A Load B Flange Web 10mm3 10mm MPa 10mm . 10mm3 10mm AS/NZS 3679.1-350 946 104 1.00 340 BS3351 115 823 134 380 PFC 1.00 966 890 340 554 772 96.6 340 849 89.0 887 45.1 46.7 340 271 426 504 49.1 221 50.4 49.1 221 44.5 320 320 1.00 MPa MPa 10mm3 300PLUS 380 PFC 946 300 PFC 250 PFC 300 320 1.00 421 230 PFC 300 320 1.00 271 200 PFC 320 1.00 180 PFC 150 PFC 1.00 129 125 PFC 100 PEC 320 320 1.00 75 PFC 320 1.00 214 • OPUS m od Grade 250 as the base grade for the sections in 1994 300PLUS head sections are produd lowed the minimumquirements of ASINS36791-300 182 44.1 44,8 44.9 38.5 22.8 320 320 250 PFC 230 PEC 200 PFC 180 PFC 150 PFC 125 PFC 100 PFC 75 PFC 1,00 728 40.3 38.5 22.8 HRSSP 4″ Ed. April 2007 38.5 22.5 12.0 6.84 320 120 6,84 1.00 6.84 1. 2 For 300PLUS sec For Grade 30 sections the leshstrength ) is 440 MP is 430 MPa LoadA0 Loud SHEAR CENTRE ã onesteel market mills
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