diff --git a/book/basics/wood/material_characteristics.ipynb b/book/basics/wood/material_characteristics.ipynb index 407421c..e30db9e 100644 --- a/book/basics/wood/material_characteristics.ipynb +++ b/book/basics/wood/material_characteristics.ipynb @@ -86,17 +86,100 @@ "|----------------------------|-----|-----|-----|\n", "| Solid Timber and Glued Laminated Timber | 0.60 | 0.80 | 2.00 |\n", "\n", - "\n", "## Material properties: solid timber\n", "\n", + "| Material property | C14 | C16 | C18 | C20 | C22 | C24 | C27 | C30 | C35 |\n", + "|--------------|------|------|------|------|------|------|------|------|------|\n", + "| Bending $f_{m;k}$ (N/mm²) | 14 | 16 | 18 | 20 | 22 | 24 | 27 | 30 | 35 |\n", + "| Tension $f_{t;0;k}$ // (N/mm²) | 8 | 10 | 11 | 12 | 13 | 14 | 16 | 18 | 21 |\n", + "| Tension $f_{t;90;k}$ ┴ (N/mm²) | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 |\n", + "| Compression $f_{c;0;k}$ // (N/mm²) | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 25 |\n", + "| Compression $f_{c;90;k}$ ┴ (N/mm²) | 2.0 | 2.2 | 2.2 | 2.3 | 2.4 | 2.5 | 2.6 | 2.7 | 2.8 |\n", + "| Shear $f_{v;k}$ (N/mm²) | 3.0 | 3.2 | 3.4 | 3.6 | 3.8 | 4.0 | 4.0 | 4.0 | 4.0 |\n", + "| Mean MOE $E_{0;\\text{mean}}$ (N/mm²) | 7000 | 8000 | 9000 | 9500 | 10000 | 11000 | 11500 | 12000 | 13000 |\n", + "| 5% MOE $E_{0,05}$ (N/mm²) | 4700 | 5400 | 6000 | 6400 | 6.7 | 7400 | 7700 | 8000 | 8700 |\n", + "| Mean MOE $E_{90;\\text{mean}}$ (N/mm²) | 230 | 270 | 300 | 320 | 0.33 | 370 | 380 | 400 | 430 |\n", + "| Mean shear modulus $G_{\\text{mean}}$ (N/mm²) | 440 | 500 | 560 | 590 | 630 | 690 | 720 | 750 | 810 |\n", + "| Density $\\rho_k$ (kg/m³) | 290 | 310 | 320 | 330 | 340 | 350 | 370 | 380 | 400 |\n", + "| Mean density $\\rho_{\\text{mean}}$ (kg/m³) | 350 | 370 | 380 | 390 | 410 | 420 | 450 | 460 | 480 |\n", + "\n", + "MOE = modulus of elasticity or Young’s modulus\n", + "\n", + "```{note}\n", + "Timber in strength classes C40 and C45 may not be readily available\n", + "```\n", + "\n", "## Material properties: glued laminated timber\n", "\n", - "## Material properties: solid timber\n", + "| Material property | GL24h | GL28h | GL32h |\n", + "|------------------------------------|----------|----------|----------|\n", + "| Bending $f_{m;k}$ (N/mm²) | 24 | 28 | 32 |\n", + "| Tension $f_{t;0;k}$ // (N/mm²) | 16.5 | 19.5 | 22.5 |\n", + "| Tension $f_{t;90;k}$ ┴ (N/mm²) | 0.4 | 0.45 | 0.5 |\n", + "| Compression $f_{c;0;k}$ // (N/mm²) | 24 | 26.5 | 29 |\n", + "| Compression $f_{c;90;k}$ ┴ (N/mm²) | 2.7 | 3.0 | 3.3 |\n", + "| Shear $f_{v;k}$ (N/mm²) | 2.7 | 3.2 | 3.8 |\n", + "| Mean MOE $E_{0;\\text{mean}}$ (N/mm²) | 11600 | 12600 | 13700 |\n", + "| 5% MOE $E_{0,05}$ (N/mm²) | 9400 | 10200 | 11100 |\n", + "| Mean MOE $E_{90;\\text{mean}}$ (N/mm²) | 390 | 420 | 460 |\n", + "| Mean shear modulus $G_{\\text{mean}}$ (N/mm²) | 720 | 780 | 850 |\n", + "| Density $\\rho_k$ (kg/m³) | 380 | 410 | 430 |\n", + "| Mean density $\\rho_{\\text{mean}}$ (kg/m³) | 420 | 450 | 470 |\n", + "\n", + "## Material properties continued: solid timber\n", + "\n", + "| | C40 | C45 | C50 | D18 | D24 | D30 | D35 | D40 | D50 | D60 | D70 |\n", + "|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|\n", + "| $f_{m;k}$ | 40 | 45 | 50 | 18 | 24 | 30 | 35 | 40 | 50 | 60 | 70 |\n", + "| $f_{t;0;k}$ // | 24 | 27 | 30 | 11 | 14 | 18 | 21 | 24 | 30 | 36 | 42 |\n", + "| $f_{t;90;k}$ ┴ | 0.4 | 0.4 | 0.4 | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 | 0.6 |\n", + "| $f_{c;0;k}$ // | 26 | 27 | 29 | 18 | 21 | 23 | 25 | 26 | 29 | 32 | 34 |\n", + "| $f_{c;90;k}$ ┴ | 2.9 | 3.1 | 3.2 | 7.5 | 7.8 | 8.0 | 8.1 | 8.3 | 9.3 | 10.5| 13.5|\n", + "| $f_{v;k}$ | 4.0 | 4.0 | 4.0 | 3.4 | 4.0 | 4.0 | 4.0 | 4.0 | 4.0 | 4.5 | 5.0 |\n", + "| $E_{0;\\text{mean}}$ | 14000 | 15000 | 16000 | 9500 | 10000 | 11000 | 12000 | 13000 | 14000 | 17000 | 20000 |\n", + "| $E_{0,05}$ | 9400 | 10000 | 10700 | 8000 | 8500 | 9200 | 10100 | 10900 | 11800 | 14300 | 16800 |\n", + "| $E_{90;\\text{mean}}$ | 470 | 500 | 530 | 630 | 670 | 730 | 800 | 860 | 930 | 1130 | 1330 |\n", + "| $G_{\\text{mean}}$ | 880 | 940 | 1000 | 590 | 620 | 690 | 750 | 810 | 880 | 1060 | 1250 |\n", + "| $\\rho_k$ | 420 | 440 | 460 | 475 | 485 | 530 | 540 | 550 | 620 | 700 | 900 |\n", + "| $\\rho_{\\text{mean}}$ | 500 | 520 | 550 | 570 | 580 | 640 | 650 | 660 | 750 | 840 | 1080 |\n", + "\n", "\n", "## Design values of material properties in ULS\n", "\n", + "The material properties given in the tables above are characteristic values. Depending on the local environment, use and load duration these values have to be adjusted to design values. The design value of the Young’s modulus is used to determine the force distribution in a statically indeterminate structure.\n", + "\n", + "Strength properties: \n", + "$X_d = k_{mod} \\cdot \\frac{X_k}{\\gamma_M}$\n", + "\n", + "Stiffness properties: \n", + "$E_d = \\frac{E_{mean}}{\\gamma_M}$ \n", + "$G_d = \\frac{G_{mean}}{\\gamma_M}$\n", + "\n", + "Where: \n", + "$X_d$ = Design value of strength property \n", + "$X_k$ = Characteristic value of strength property \n", + "$E_d$ = Design value of Young’s modulus \n", + "$E_{mean}$ = Characteristic value of Young’s modulus \n", + "$k_{mod}$ = modification factor \n", + "$\\gamma_M$ = model factor; 1,25 for glued laminated timber, 1,3 for solid timber and connections\n", + "\n", "## Final deflection\n", - "\n" + "\n", + "The final deflection in SLS including creep effects is defined as: \n", + "$u_{fin} = u_{fin;G} + u_{fin;Q;1} + \\Sigma u_{fin;Q;i}$ \n", + "$u_{fin;G} = u_{inst;G} \\cdot (1 + k_{def})$ \n", + "$u_{fin;Q;1} = u_{inst;Q;1} \\cdot (1 + \\psi_{2,1} \\cdot k_{def})$ \n", + "$u_{fin;Q;i} = u_{inst;Q;i} \\cdot (\\psi_0 + \\psi_{2,i} \\cdot k_{def})$ \n", + "\n", + "Where: \n", + "$u_{fin}$ = final deflection \n", + "$u_{inst}$ = instantaneous deflection \n", + "$u_G$ = deflection under permanent load \n", + "$u_{Q;1}$ = deflection under leading variable load \n", + "$u_{Q;i}$ = deflection under other variable load \n", + "$\\Psi_0$ = load combination factor (see also |general|loads|) \n", + "$\\Psi_2$ = factor for quasi permanent value of variable load i \n", + "$k_{def}$ = creep factor" ] }, {