HSS_Shape Example
See link below for the current HSS_Shapes from the AISC v16 steel database.
Constructing a HSS_Shape:
Before constructing, import the AISCSteel package. Also import the StructuralUnits package since we will use it later on.
using StructuralUnits
import AISCSteel
import AISCSteel.Shapes.HSS_Shapes as hssNow that the package has been imported, lets construct a HSS10x6x3/16.
hss_shape = hss.HSS_Shape("HSS10x6x3/16")AISCSteel.Shapes.HSS_Shapes.HSS_Shape("HSS10X6X3/16", 19.63 plf, 5.37 inch^2, 10.0 inch, 9.48 inch, 6.0 inch, 5.48 inch, 0.1875 inch, 0.174 inch, 74.6 inch^4, 18.0 inch^3, 14.9 inch^3, 3.73 inch, 34.1 inch^4, 12.7 inch^3, 11.4 inch^3, 2.52 inch, 73.8 inch^4, 19.9 inch^3, 29000.0 ksi, 50.0 ksi)The following went and searched through the AISC v16 steel database and pulled the relevant info to construct a HSS_Shape. You can now access information in the struct like so:
The overall width of the shape:
hss_shape.B6.0 inchThe weight of the HSS_Shape:
hss_shape.weight19.63 plfCompression Capacity of HSS_Shape:
See link below for the available functions relating to compression for the HSS_Shape member:
We can calculate the compressive capacity of the HSS10x6x3/16 shape we just constructed:
L_cx = L_cy = 12ft
ϕ_c = 0.9
P_n = hss.Compression.calc_Pn(hss_shape, L_cx, L_cy)
ϕP_n = ϕ_c * P_n164.2622466285979 kipLets see what the calc_Pn function did:
using Handcalcs
set_handcalcs(precision=2) # sets number of decimals displayed
@handcalcs P_n = hss.Compression.calc_Pn(hss_shape, L_cx, L_cy)\[\begin{aligned} b &= b = 5.48\;\mathrm{inch} \\[10pt] t &= t_{des} = 0.17\;\mathrm{inch} \\[10pt] \lambda &= \frac{b}{t} = \frac{5.48\;\mathrm{inch}}{0.17\;\mathrm{inch}} = 31.49 \\[10pt] \lambda_{r} &= 1.4 \cdot \sqrt{\frac{E}{F_{y}}} = 1.4 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 33.72 \\[10pt] \text{Since: }\lambda \leq \lambda_{r} &= 31.49 \leq 33.72 = true \\[10pt] \lambda_{class} &= nonslender \\[10pt] b &= h = 9.48\;\mathrm{inch} \\[10pt] t &= t_{des} = 0.17\;\mathrm{inch} \\[10pt] \lambda &= \frac{b}{t} = \frac{9.48\;\mathrm{inch}}{0.17\;\mathrm{inch}} = 54.48 \\[10pt] \lambda_{r} &= 1.4 \cdot \sqrt{\frac{E}{F_{y}}} = 1.4 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 33.72 \\[10pt] \text{Since: }\lambda \leq \lambda_{r} &= 54.48 \leq 33.72 = false \\[10pt] \lambda_{class} &= slender \\[10pt] \text{Since: }\frac{L_{cx}}{r_{x}} > \frac{L_{cy}}{r_{y}} &= \frac{12\;\mathrm{ft}}{3.73\;\mathrm{inch}} > \frac{12\;\mathrm{ft}}{2.52\;\mathrm{inch}} = false \\[10pt] L_{c} &= L_{cy} = 12\;\mathrm{ft} \\[10pt] r &= r_{y} = 2.52\;\mathrm{inch} \\[10pt] F_{e} &= \frac{\pi^{2} \cdot E}{\left( \frac{L_{c}}{r} \right)^{2}} = \frac{3.14^{2} \cdot 29000\;\mathrm{ksi}}{\left( \frac{12\;\mathrm{ft}}{2.52\;\mathrm{inch}} \right)^{2}} = 87.65\;\mathrm{ksi} \\[10pt] \text{Since: }\frac{L_{c}}{r} \leq 4.71 \cdot \sqrt{\frac{E}{F_{y}}} &= \frac{12\;\mathrm{ft}}{2.52\;\mathrm{inch}} \leq 4.71 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = true \\[10pt] F_{n} &= 0.66^{\frac{F_{y}}{F_{e}}} \cdot F_{y} = 0.66^{\frac{50\;\mathrm{ksi}}{87.65\;\mathrm{ksi}}} \cdot 50\;\mathrm{ksi} = 39.38\;\mathrm{ksi} \\[10pt] \text{Since: }\lambda_{hclass} &= nonslender = slender = false \\[10pt] \text{Since: }\lambda_{bclass} &= nonslender = true \\[10pt] b &= h = 9.48\;\mathrm{inch} \\[10pt] t &= t_{des} = 0.17\;\mathrm{inch} \\[10pt] c_{1} &= 0.2 \\[10pt] c_{2} &= 1.38 \\[10pt] F_{el} &= \left( c_{2} \cdot \frac{\lambda_{r}}{\lambda} \right)^{2} \cdot F_{y} = \left( 1.38 \cdot \frac{33.72}{54.48} \right)^{2} \cdot 50\;\mathrm{ksi} = 36.47\;\mathrm{ksi} \\[10pt] \text{Since: }\lambda \leq \lambda_{r} \cdot \sqrt{\frac{F_{y}}{F_{n}}} &= 54.48 \leq 33.72 \cdot \sqrt{\frac{50\;\mathrm{ksi}}{39.38\;\mathrm{ksi}}} = false \\[10pt] b_{e} &= b \cdot \left( 1 - c_{1} \cdot \sqrt{\frac{F_{el}}{F_{n}}} \right) \cdot \sqrt{\frac{F_{el}}{F_{n}}} = 9.48\;\mathrm{inch} \cdot \left( 1 - 0.2 \cdot \sqrt{\frac{36.47\;\mathrm{ksi}}{39.38\;\mathrm{ksi}}} \right) \cdot \sqrt{\frac{36.47\;\mathrm{ksi}}{39.38\;\mathrm{ksi}}} = 7.37\;\mathrm{inch} \\[10pt] A_{e} &= A_{g} - 2 \cdot \left( b - b_{e} \right) \cdot t = 5.37\;\mathrm{inch}^{2} - 2 \cdot \left( 9.48\;\mathrm{inch} - 7.37\;\mathrm{inch} \right) \cdot 0.17\;\mathrm{inch} = 4.63\;\mathrm{inch}^{2} \\[10pt] P_{n} &= F_{n} \cdot A_{e} = 39.38\;\mathrm{ksi} \cdot 4.63\;\mathrm{inch}^{2} = 182.51\;\mathrm{kip} \end{aligned}\]
Flexure Capacity of HSS_Shape:
See link below for the available functions relating to flexure for the HSS_Shape member:
Major Axis Bending
We can calculate the flexural capacity about the x-axis of the HSS10x6x3/16 shape we just constructed:
L_b = 21ft
ϕ_b = 0.9
C_b = 1.14
M_nx = hss.Flexure.calc_Mnx(hss_shape, L_b, C_b)
ϕM_nx = ϕ_b * M_nx59.70594936286428 ft kipLets see what the calc_Mnx function did:
@handcalcs M_nx = hss.Flexure.calc_Mnx(hss_shape, L_b, C_b)\[\begin{aligned} \lambda &= \frac{b}{t} = \frac{5.48\;\mathrm{inch}}{0.17\;\mathrm{inch}} = 31.49 \\[10pt] \lambda_{p} &= 1.12 \cdot \sqrt{\frac{E}{F_{y}}} = 1.12 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 26.97 \\[10pt] \lambda_{r} &= 1.4 \cdot \sqrt{\frac{E}{F_{y}}} = 1.4 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 33.72 \\[10pt] \text{Since: }\lambda_{p} < \lambda \leq \lambda_{r} &= 26.97 < 31.49 \leq 33.72 = true \\[10pt] \lambda_{class} &= noncompact \\[10pt] \lambda &= \frac{h}{t} = \frac{9.48\;\mathrm{inch}}{0.17\;\mathrm{inch}} = 54.48 \\[10pt] \lambda_{p} &= 2.42 \cdot \sqrt{\frac{E}{F_{y}}} = 2.42 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 58.28 \\[10pt] \lambda_{r} &= 5.7 \cdot \sqrt{\frac{E}{F_{y}}} = 5.7 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 137.27 \\[10pt] \text{Since: }\lambda \leq \lambda_{p} &= 54.48 \leq 58.28 = true \\[10pt] \lambda_{class} &= compact \\[10pt] M_{p} &= F_{y} \cdot Z = 50\;\mathrm{ksi} \cdot 18\;\mathrm{inch}^{3} = 75\;\mathrm{ft}\,\mathrm{kip} \\[10pt] a_{w} &= \frac{2 \cdot h \cdot t_{w}}{b \cdot t_{f}} = \frac{2 \cdot 9.48\;\mathrm{inch} \cdot 0.17\;\mathrm{inch}}{5.48\;\mathrm{inch} \cdot 0.17\;\mathrm{inch}} = 3.46 \\[10pt] h_{c} &= h = 9.48\;\mathrm{inch} \\[10pt] R_{pg} &= 1 - \frac{a_{w}}{1200 + 300 \cdot a_{w}} \cdot \left( \frac{h_{c}}{t_{w}} - 5.7 \cdot \sqrt{\frac{E}{F_{y}}} \right) = 1 - \frac{3.46}{1200 + 300 \cdot 3.46} \cdot \left( \frac{9.48\;\mathrm{inch}}{0.17\;\mathrm{inch}} - 5.7 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} \right) = 1.13 \\[10pt] R_{pg} &= \mathrm{min}\left( R_{pg}, 1 \right) = \mathrm{min}\left( 1.13, 1 \right) = 1 \\[10pt] L_{p} &= \frac{0.13 \cdot E \cdot r_{y} \cdot \sqrt{J \cdot A_{g}}}{M_{p}} = \frac{0.13 \cdot 29000\;\mathrm{ksi} \cdot 2.52\;\mathrm{inch} \cdot \sqrt{73.8\;\mathrm{inch}^{4} \cdot 5.37\;\mathrm{inch}^{2}}}{75\;\mathrm{ft}\,\mathrm{kip}} = 17.51\;\mathrm{ft} \\[10pt] L_{r} &= \frac{2 \cdot E \cdot r_{y} \cdot \sqrt{J \cdot A_{g}}}{0.7 \cdot F_{y} \cdot S_{x}} = \frac{2 \cdot 29000\;\mathrm{ksi} \cdot 2.52\;\mathrm{inch} \cdot \sqrt{73.8\;\mathrm{inch}^{4} \cdot 5.37\;\mathrm{inch}^{2}}}{0.7 \cdot 50\;\mathrm{ksi} \cdot 14.9\;\mathrm{inch}^{3}} = 464.95\;\mathrm{ft} \\[10pt] M_{nFY} &= M_{p} = 75\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }\lambda_{fclass} &= noncompact = true \\[10pt] M_{nFLB} &= M_{p} - \left( M_{p} - F_{y} \cdot S \right) \cdot \frac{\lambda_{f} - \lambda_{pf}}{\lambda_{rf} - \lambda_{pf}} = 75\;\mathrm{ft}\,\mathrm{kip} - \left( 75\;\mathrm{ft}\,\mathrm{kip} - 50\;\mathrm{ksi} \cdot 14.9\;\mathrm{inch}^{3} \right) \cdot \frac{31.49 - 26.97}{33.72 - 26.97} = 66.34\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }\lambda_{wclass} &= compact = true \\[10pt] M_{nFLB} &= M_{p} = 75\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }L_{p} < L_{b} \leq L_{r} &= 17.51\;\mathrm{ft} < 21\;\mathrm{ft} \leq 464.95\;\mathrm{ft} = true \\[10pt] M_{nLTB} &= C_{b} \cdot \left( M_{p} - \left( M_{p} - 0.7 \cdot F_{y} \cdot S_{x} \right) \cdot \frac{L_{b} - L_{p}}{L_{r} - L_{p}} \right) = 1.14 \cdot \left( 75\;\mathrm{ft}\,\mathrm{kip} - \left( 75\;\mathrm{ft}\,\mathrm{kip} - 0.7 \cdot 50\;\mathrm{ksi} \cdot 14.9\;\mathrm{inch}^{3} \right) \cdot \frac{21\;\mathrm{ft} - 17.51\;\mathrm{ft}}{464.95\;\mathrm{ft} - 17.51\;\mathrm{ft}} \right) = 85.22\;\mathrm{ft}\,\mathrm{kip} \\[10pt] M_{n} &= \mathrm{min}\left( M_{nY}, M_{nFLB}, M_{nWLB}, M_{nLTB} \right) = \mathrm{min}\left( 75\;\mathrm{ft}\,\mathrm{kip}, 66.34\;\mathrm{ft}\,\mathrm{kip}, 75\;\mathrm{ft}\,\mathrm{kip}, 85.22\;\mathrm{ft}\,\mathrm{kip} \right) = 66.34\;\mathrm{ft}\,\mathrm{kip} \end{aligned}\]
Minor Axis Bending
We can calculate the flexural capacity about the y-axis of the HSS10x6x3/16 shape we just constructed:
M_ny = hss.Flexure.calc_Mny(hss_shape)
ϕM_ny = ϕ_b * M_ny32.33912878030443 ft kipLets see what the calc_Mny function did:
@handcalcs M_ny = hss.Flexure.calc_Mny(hss_shape)\[\begin{aligned} \lambda &= \frac{b}{t} = \frac{9.48\;\mathrm{inch}}{0.17\;\mathrm{inch}} = 54.48 \\[10pt] \lambda_{p} &= 1.12 \cdot \sqrt{\frac{E}{F_{y}}} = 1.12 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 26.97 \\[10pt] \lambda_{r} &= 1.4 \cdot \sqrt{\frac{E}{F_{y}}} = 1.4 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 33.72 \\[10pt] \text{Since: }\lambda \leq \lambda_{p} &= 54.48 \leq 26.97 = false \\[10pt] \lambda_{p} < \lambda \leq \lambda_{r} &= 26.97 < 54.48 \leq 33.72 = false \\[10pt] \lambda_{class} &= slender \\[10pt] \lambda &= \frac{h}{t} = \frac{5.48\;\mathrm{inch}}{0.17\;\mathrm{inch}} = 31.49 \\[10pt] \lambda_{p} &= 2.42 \cdot \sqrt{\frac{E}{F_{y}}} = 2.42 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 58.28 \\[10pt] \lambda_{r} &= 5.7 \cdot \sqrt{\frac{E}{F_{y}}} = 5.7 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} = 137.27 \\[10pt] \text{Since: }\lambda \leq \lambda_{p} &= 31.49 \leq 58.28 = true \\[10pt] \lambda_{class} &= compact \\[10pt] M_{p} &= F_{y} \cdot Z = 50\;\mathrm{ksi} \cdot 12.7\;\mathrm{inch}^{3} = 52.92\;\mathrm{ft}\,\mathrm{kip} \\[10pt] a_{w} &= \frac{2 \cdot h \cdot t_{w}}{b \cdot t_{f}} = \frac{2 \cdot 5.48\;\mathrm{inch} \cdot 0.17\;\mathrm{inch}}{9.48\;\mathrm{inch} \cdot 0.17\;\mathrm{inch}} = 1.16 \\[10pt] h_{c} &= h = 5.48\;\mathrm{inch} \\[10pt] R_{pg} &= 1 - \frac{a_{w}}{1200 + 300 \cdot a_{w}} \cdot \left( \frac{h_{c}}{t_{w}} - 5.7 \cdot \sqrt{\frac{E}{F_{y}}} \right) = 1 - \frac{1.16}{1200 + 300 \cdot 1.16} \cdot \left( \frac{5.48\;\mathrm{inch}}{0.17\;\mathrm{inch}} - 5.7 \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} \right) = 1.08 \\[10pt] R_{pg} &= \mathrm{min}\left( R_{pg}, 1 \right) = \mathrm{min}\left( 1.08, 1 \right) = 1 \\[10pt] M_{nFY} &= M_{p} = 52.92\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }\lambda_{fclass} &= compact = slender = false \\[10pt] \lambda_{fclass} &= noncompact = slender = false \\[10pt] b_{e} &= 1.92 \cdot t_{f} \cdot \sqrt{\frac{E}{F_{y}}} \cdot \left( 1 - \frac{0.38}{\frac{b}{t_{f}}} \cdot \sqrt{\frac{E}{F_{y}}} \right) = 1.92 \cdot 0.17\;\mathrm{inch} \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} \cdot \left( 1 - \frac{0.38}{\frac{9.48\;\mathrm{inch}}{0.17\;\mathrm{inch}}} \cdot \sqrt{\frac{29000\;\mathrm{ksi}}{50\;\mathrm{ksi}}} \right) = 6.69\;\mathrm{inch} \\[10pt] b &= b - b_{e} = 9.48\;\mathrm{inch} - 6.69\;\mathrm{inch} = 2.79\;\mathrm{inch} \\[10pt] a &= b \cdot t_{f} = 2.79\;\mathrm{inch} \cdot 0.17\;\mathrm{inch} = 0.48\;\mathrm{inch}^{2} \\[10pt] d &= \frac{Ht - t_{f}}{2} = \frac{6\;\mathrm{inch} - 0.17\;\mathrm{inch}}{2} = 2.91\;\mathrm{inch} \\[10pt] I_{e} &= I - 2 \cdot \left( \frac{b \cdot t_{f}^{3}}{12} + a \cdot d^{2} \right) = 34.1\;\mathrm{inch}^{4} - 2 \cdot \left( \frac{2.79\;\mathrm{inch} \cdot \left( 0.17\;\mathrm{inch} \right)^{3}}{12} + 0.48\;\mathrm{inch}^{2} \cdot \left( 2.91\;\mathrm{inch} \right)^{2} \right) = 25.87\;\mathrm{inch}^{4} \\[10pt] S_{e} &= \frac{I_{e}}{\frac{Ht}{2}} = \frac{25.87\;\mathrm{inch}^{4}}{\frac{6\;\mathrm{inch}}{2}} = 8.62\;\mathrm{inch}^{3} \\[10pt] M_{nFLB} &= F_{y} \cdot S_{e} = 50\;\mathrm{ksi} \cdot 8.62\;\mathrm{inch}^{3} = 35.93\;\mathrm{ft}\,\mathrm{kip} \\[10pt] \text{Since: }\lambda_{wclass} &= compact = true \\[10pt] M_{nFLB} &= M_{p} = 52.92\;\mathrm{ft}\,\mathrm{kip} \\[10pt] M_{n} &= \mathrm{min}\left( M_{nY}, M_{nFLB}, M_{nWLB} \right) = \mathrm{min}\left( 52.92\;\mathrm{ft}\,\mathrm{kip}, 35.93\;\mathrm{ft}\,\mathrm{kip}, 52.92\;\mathrm{ft}\,\mathrm{kip} \right) = 35.93\;\mathrm{ft}\,\mathrm{kip} \end{aligned}\]