xxxxxxxxxx# ๅๅ
ฌๆฅผ็จๅบๅ่ฎก็ฎไนฆโ้ฉฌๅ
โๆฌ่ฎก็ฎไนฆ็ผๅไนๅไป
็จไบๅ
้จๅฟซ้่ฏ็ฎใ่ฎพ่ฎกใ้ช็ฎไน็จ๏ผๆชๆพ่่ๅ
ฌ็คบ็ฒๆนไน็จใ่ฝๅบ่ฆๆฑๅขๅ Latexๅ
ฌๅผ่กไพฟไบ้
่ฏป๏ผๅฆไปๆไธไพฟ่ฟ่ฏท่ฐ
่งฃใโ้ค้้ขๅคๆ ๆณจ๏ผๆฌ่ฎก็ฎไนฆไฝฟ็จๅฝ้
ๆ ๅๅไฝSIใโๆฌ่ฎก็ฎไนฆๅทฒ็ป่ฟSAP2000้ช็ฎ๏ผ็ปๆ่ง้ใๅๅ ฌๆฅผ็จๅบๅ่ฎก็ฎไนฆยถ
้ฉฌๅ
ๆฌ่ฎก็ฎไนฆ็ผๅไนๅไป ็จไบๅ ้จๅฟซ้่ฏ็ฎใ่ฎพ่ฎกใ้ช็ฎไน็จ๏ผๆชๆพ่่ๅ ฌ็คบ็ฒๆนไน็จใ่ฝๅบ่ฆๆฑๅขๅ Latexๅ ฌๅผ่กไพฟไบ้ ่ฏป๏ผๅฆไปๆไธไพฟ่ฟ่ฏท่ฐ ่งฃใ
้ค้้ขๅคๆ ๆณจ๏ผๆฌ่ฎก็ฎไนฆไฝฟ็จๅฝ้ ๆ ๅๅไฝSIใ
ๆฌ่ฎก็ฎไนฆๅทฒ็ป่ฟSAP2000้ช็ฎ๏ผ็ปๆ่ง้ใ
In [1]:
xxxxxxxxxxfrom IPython.display import display, Markdown, Latex, Mathโ# https://dev.to/callas1900/how-to-display-latex-matrix-as-output-of-a-code-cell-40ckdef latex_matrix(array): data = '' for line in array: if type(line) == type([1]) or type(line) == type([1.1]) or type(line) == type(np.float64(1)): data += ' %.3E &'%line + r' \\' continue if len(line) == 1: data += ' %.3E &'%line + r' \\\r' continue for element in line: data += ' %.3E &'%element data += r' \\' + '\n' #display(Math('\\begin{bmatrix} \n%s\end{bmatrix}'%data)) return '\\begin{bmatrix} \n%s\end{bmatrix}'%dataโfrom IPython.core.display import HTMLHTML("""<style>div.output_latex { text-align: center;}โ.jp-OutputArea-output.jp-RenderedLatex { text-align: center;}โdiv.output_area .MathJax_Display { text-align: center !important;}โdiv.jp-InputArea { display: none;}โ</style>""")Out[1]:
xxxxxxxxxx## 1 ๆกๆถๅธ็ฝฎโไธปๆข xๆนๅ 5m x 6่ทจ = 30mโไธปๆข yๆนๅ 8m x 2่ทจ = 16mโๆฌกๆข xๆนๅ 1.6m x 5่ทจๆฏๆฆ1 ๆกๆถๅธ็ฝฎยถ
ไธปๆข xๆนๅ 5m x 6่ทจ = 30m
ไธปๆข yๆนๅ 8m x 2่ทจ = 16m
ๆฌกๆข xๆนๅ 1.6m x 5่ทจๆฏๆฆ
In [2]:
xxxxxxxxxxframe_x = 30frame_y = 16frame_z = 10frame_x_span = 5frame_x_span_n = frame_x/frame_x_spanframe_y_span = 8frame_y_span_n = frame_y/frame_y_spanframe_y_sub_span = 1.6frame_y_sub_span_n = frame_y_span/frame_y_sub_spanโframe_zs = [4,3,4]frame_z_abss = [4,7,10]frame_z_1 = frame_zs[0]frame_z_2 = frame_zs[1]frame_z_3 = frame_zs[2]xxxxxxxxxx## 2 ่ท่ฝฝ่ฎก็ฎโ### 2.1 ๆดป่ท่ฝฝโ#### 2.1.1 ๅๅ
ฌๆฅผ้ขๆดป่ท่ฝฝโๆ นๆฎGB50009-2012 p14โ$$2kN/m^2$$โ$$\psi_c = 0.7$$โ$$\psi_f = 0.5$$โ$$\psi_q = 0.4$$โ#### 2.1.2 ไธไธไบบๅฑ้ขๆดป่ท่ฝฝโๆ นๆฎGB50009-2012 p18โ$$0.5kN/m^2$$โ$$\psi_c = 0.7$$โ$$\psi_f = 0.5$$โ$$\psi_q = 0$$โ#### 2.1.3 ้ช่ท่ฝฝโ[้ช่ท่ฝฝๅๅบ](https://www.dlubal.com/zh/solutions/online-services/load-zones)โๆ นๆฎGB50009-2012 p26โ$$s_0 = 0.5kN/m^2$$โ$$\mu_r = 1$$โ$$s_k = \mu_r s_0 = 0.5kN/m^2$$In [3]:
xxxxxxxxxxliveload_floor_perarea = 2000liveload_roof_perarea = 500liveload_snow_perarea = 500xxxxxxxxxx### 2.2 ๆ่ท่ฝฝโ#### 2.2.1 ่ฝป่ดจๆททๅๅๆฅผๆฟโๅๅๆฟ 100ๅ่ฝป่ดจๆททๅๅๆ นๆฎ[ๆๅ
ฌๅธๆฐๆฎ](http://www.yzjz169.com/news/hydt/308.html)๏ผไฟๅฎ่ฎพ่ฎกๅๅผ850 kg/m3,ๅณ85kg/m2๏ผๆๅฎๅ
จๅ1.2e3kg/m3 - ่โ็ฑ[่ธๅๅ ๆฐๆททๅๅๆฅผๆฟ(alcๆฅผๆฟ)](https://www.hnalcb.cn/cp/e/57.html)๏ผ1.6m่ทจ้ฟๆฟ่ฝฝๅ5kN/m2โ20ๅๆฐดๆณฅ็ ๆตๆพๅนณ 2e3kg/m3๏ผๅณ40kg/m210ๅๅฐ็ 2.5e3kg/m3๏ผๅณ25kg/m2ๆๆจๅฐๆฟ10kg/m2โๆป่ดจ้ๆ่พๅคงๅผ2.2 ๆ่ท่ฝฝยถ
2.2.1 ่ฝป่ดจๆททๅๅๆฅผๆฟยถ
ๅๅๆฟ 100ๅ่ฝป่ดจๆททๅๅๆ นๆฎๆๅ ฌๅธๆฐๆฎ๏ผไฟๅฎ่ฎพ่ฎกๅๅผ850 kg/m3,ๅณ85kg/m2๏ผๆๅฎๅ จๅ1.2e3kg/m3 - ่
็ฑ่ธๅๅ ๆฐๆททๅๅๆฅผๆฟ(alcๆฅผๆฟ)๏ผ1.6m่ทจ้ฟๆฟ่ฝฝๅ5kN/m2
20ๅๆฐดๆณฅ็ ๆตๆพๅนณ 2e3kg/m3๏ผๅณ40kg/m2 10ๅๅฐ็ 2.5e3kg/m3๏ผๅณ25kg/m2 ๆๆจๅฐๆฟ10kg/m2
ๆป่ดจ้ๆ่พๅคงๅผ
In [4]:
xxxxxxxxxxclass Material: def __init__(self, density=0, E = 0): self.density = density self.E = EIn [5]:
xxxxxxxxxxmaterial_lightconcrete = Material(density=1200)material_cement = Material(density=2000)material_tile = Material(density=2500)material_glubam = Material(density=750, E = 1e10)In [6]:
xxxxxxxxxxclass Layer: def __init__(self, material, thickness=0): self.mass_perarea = material.density * thicknessxxxxxxxxxx็ป่ฎก็ฎ๏ผๆฏๅนณๆน็ฑณ่ดจ้็ป่ฎก็ฎ๏ผๆฏๅนณๆน็ฑณ่ดจ้
In [7]:
xxxxxxxxxxfloor_layer_lightconcrete = Layer(material_lightconcrete, thickness=0.1)floor_layer_cement = Layer(material_cement, thickness=0.02)floor_layer_tile = Layer(material_tile, thickness=0.01)โmass_floor_perarea = floor_layer_lightconcrete.mass_perarea\ + floor_layer_cement.mass_perarea\ + floor_layer_tile.mass_perareamass_floor_perareadisplay(Markdown('$$m=\sum{m_i}='+str(mass_floor_perarea)+'$$'))In [8]:
xxxxxxxxxxclass Beam: def __init__(self, material, crosec_width, crosec_height, length=1): self.crosec_width = crosec_width self.crosec_height = crosec_height self.length = length self.A = crosec_width * crosec_height self.density_perlength = material.density * self.A self.I = crosec_width * crosec_height ** 3 /12โbeam_sub = Beam(material_glubam, 0.12, 0.36)beam = Beam(material_glubam, 0.3, 0.6)column = Beam(material_glubam, 0.3, 0.5)xxxxxxxxxxๆ นๆฎGB50009-2012 3.2.4โ่ท่ฝฝ่ฎพ่ฎกๅผโ$$S_d = \max(1.2\sum{G}+1.4\sum{Q}, 1.35\sum{G}+1.4\times0.7Q)$$โ่ท่ฝฝๆ ๅๅผโ$$S_s = \sum{G}+Q_1+0.7\sum{Q_i}, (i>1)$$ๆ นๆฎGB50009-2012 3.2.4
่ท่ฝฝ่ฎพ่ฎกๅผ
่ท่ฝฝๆ ๅๅผ
In [9]:
xxxxxxxxxxg = 9.8def designload(deadload,liveload): return max( 1.2*sum(deadload) + 1.4*sum(liveload), 1.35*sum(deadload) + 1.4*0.7*sum(liveload), )def standardload(deadload,liveload): return sum(deadload)+0.3*liveload[0]+0.7*sum(liveload)xxxxxxxxxx### 3.1 ่ฝป่ดจๆททๅๅๆฅผๆฟโๅๅๅธ่ท่ฝฝ3.1 ่ฝป่ดจๆททๅๅๆฅผๆฟยถ
ๅๅๅธ่ท่ฝฝ
In [10]:
xxxxxxxxxxdeadload_floor_perarea = mass_floor_perarea * gdesignload_floor_perarea = designload([deadload_floor_perarea], [liveload_floor_perarea])โdesignload_floor_perareadisplay(Markdown('$$S_d='+str(designload_floor_perarea)+'$$'))xxxxxxxxxxๅฐไบ5kNๅฐไบ5kN
xxxxxxxxxxไฝฟ็จ็ไฝฟ็จ็
In [11]:
xxxxxxxxxxdesignload_floor_perarea/5000display(Markdown('$$utilization='+str(designload_floor_perarea/5000)+'$$'))In [12]:
xxxxxxxxxxdeadload_beam_sub_perlength = deadload_floor_perarea * frame_y_sub_span\ + beam_sub.density_perlength * gliveload_beam_sub_perlength = liveload_floor_perarea * frame_y_sub_spanxxxxxxxxxx#### 3.2.1 ้ช็ฎๆฟ่ฝฝๅโ$$\sigma=\cfrac{My}{I}<[\sigma]$$โๅ
ถไธญโ$$M = \cfrac{qL^2}{8}$$In [13]:
xxxxxxxxxxdesignload_beam_sub_perlength = designload([deadload_beam_sub_perlength], [liveload_beam_sub_perlength])max_moment_beam_sub = designload_beam_sub_perlength*frame_y_sub_span**2/8max_sigma_beam_sub = max_moment_beam_sub*beam_sub.crosec_height/2/beam_sub.Imax_sigma_beam_subdisplay(Markdown('$$\sigma='+str(max_sigma_beam_sub)+'$$'))xxxxxxxxxxๅฐไบglubamๆๆๅผบๅบฆโๆ Y. Wu, Y. Xiao, Steel and glubam hybrid space truss, Engineering Structures 171, 2018, p140, ๅ
ถไปๆๆๅๅญฆๆง่ดจๅโ$$[\sigma] = 1.06e8$$ๅฐไบglubamๆๆๅผบๅบฆ
ๆ Y. Wu, Y. Xiao, Steel and glubam hybrid space truss, Engineering Structures 171, 2018, p140, ๅ ถไปๆๆๅๅญฆๆง่ดจๅ
xxxxxxxxxxไฝฟ็จ็ไฝฟ็จ็
In [14]:
xxxxxxxxxxmax_sigma_beam_sub/1.06e8display(Markdown('$$utilization='+str(max_sigma_beam_sub/1.06e8)+'$$'))xxxxxxxxxx#### 3.2.2 ้ช็ฎๆญฃๅธธไฝฟ็จๆ้็ถๆไฝ็งปโ$$u = \cfrac{5qL^4}{384EI}< [u] = \cfrac{1}{250}L$$In [15]:
xxxxxxxxxxstandardload_beam_sub_perlength = standardload([deadload_beam_sub_perlength], [liveload_beam_sub_perlength])โdef disp_distributed_load(q,L,E,I): return 5*q*L**4/384/E/Iโmax_disp_beam_sub = disp_distributed_load(standardload_beam_sub_perlength, frame_x_span, material_glubam.E, beam_sub.I)max_disp_beam_subdisplay(Markdown('$$u='+str(max_disp_beam_sub)+'$$'))xxxxxxxxxxๅฐไบ้ๅผๅฐไบ้ๅผ
In [16]:
xxxxxxxxxxframe_x_span/250display(Markdown('$$[u]='+str(frame_x_span/250)+'$$'))xxxxxxxxxxไฝฟ็จ็ไฝฟ็จ็
In [17]:
xxxxxxxxxxmax_disp_beam_sub / (frame_x_span/250)display(Markdown('$$utilization='+str(max_disp_beam_sub / (frame_x_span/250))+'$$'))In [18]:
xxxxxxxxxxdeadload_beam_perlength = deadload_floor_perarea * frame_x_span\ + beam_sub.density_perlength * frame_x_span * (frame_y_sub_span_n-1) * g\ + beam.density_perlength * gliveload_beam_perlength = liveload_floor_perarea * frame_x_spanIn [19]:
xxxxxxxxxxdesignload_beam_perlength = designload([deadload_beam_perlength], [liveload_beam_perlength])max_moment_beam = designload_beam_perlength*frame_x_span**2/8max_sigma_beam = max_moment_beam*beam.crosec_height/2/beam.Imax_sigma_beamdisplay(Markdown('$$\sigma='+str(max_sigma_beam)+'$$'))xxxxxxxxxxๅฐไบglubamๆๆๅผบๅบฆโ$$[\sigma] = 65.3e6$$ๅฐไบglubamๆๆๅผบๅบฆ
xxxxxxxxxxไฝฟ็จ็ไฝฟ็จ็
In [20]:
xxxxxxxxxxmax_sigma_beam/65.3e6display(Markdown('$$utilization='+str(max_sigma_beam/65.3e6)+'$$'))xxxxxxxxxx#### 3.3.2 ้ช็ฎๆญฃๅธธไฝฟ็จๆ้็ถๆไฝ็งป3.3.2 ้ช็ฎๆญฃๅธธไฝฟ็จๆ้็ถๆไฝ็งปยถ
In [21]:
xxxxxxxxxxstandardload_beam_perlength = standardload([deadload_beam_perlength], [liveload_beam_perlength])โdef disp_distributed_load(q,L,E,I): return 5*q*L**4/384/E/Iโmax_disp_beam = disp_distributed_load(standardload_beam_perlength, frame_y_span, material_glubam.E, beam.I)max_disp_beamdisplay(Markdown('$$u='+str(max_disp_beam)+'$$'))xxxxxxxxxxๅฐไบ้ๅผๅฐไบ้ๅผ
In [22]:
xxxxxxxxxxframe_y_span/250display(Markdown('$$u='+str(frame_y_span/250)+'$$'))xxxxxxxxxxไฝฟ็จ็ไฝฟ็จ็
In [23]:
xxxxxxxxxxmax_disp_beam / (frame_y_span/250)display(Markdown('$$utilization='+str(max_disp_beam / (frame_y_span/250))+'$$'))xxxxxxxxxx### 3.4 ๆฑโ2ๆฅผใ3ๆฅผใๅฑ้ขๆๆฅผ้ขๆ่ฝฝ๏ผ2ๆฅผใ3ๆฅผๆๅๅ
ฌๆฅผๆดป่ฝฝ๏ผๅฑ้ขๆ้ช่ท่ฝฝโๅๅฑๆฑ่ท่ฝฝๅฆไธ3.4 ๆฑยถ
2ๆฅผใ3ๆฅผใๅฑ้ขๆๆฅผ้ขๆ่ฝฝ๏ผ2ๆฅผใ3ๆฅผๆๅๅ ฌๆฅผๆดป่ฝฝ๏ผๅฑ้ขๆ้ช่ท่ฝฝ
ๅๅฑๆฑ่ท่ฝฝๅฆไธ
In [24]:
xxxxxxxxxxdeadload_perstory = deadload_floor_perarea * frame_x * frame_y\ + (beam_sub.density_perlength * frame_x * (frame_y_sub_span_n-1) * frame_y_span_n\ + beam.density_perlength * frame_x * (frame_y_span_n+1) \ + beam.density_perlength * frame_y * (frame_x_span_n+1))*gโdeadload_roof_perarea = 500โdeadload_roof = deadload_roof_perarea * frame_x * frame_yโliveload_perstory = liveload_floor_perarea * frame_x * frame_yโliveload_snow = liveload_snow_perarea * frame_x * frame_yโliveload_roof = liveload_roof_perarea * frame_x * frame_yโ# 3ๆฅผ (ๆๆฃ้คไธไพง่พนๆฑ)โdeadload_columns_only_3 = (column.density_perlength * frame_z_3 * (frame_x_span_n+1) * (frame_y_span_n+1)) * gโdeadload_columns_3 = deadload_roof + deadload_columns_only_3โliveload_columns_3 = liveload_roof designload_columns_3 = designload([deadload_columns_3], [liveload_roof, liveload_snow])standardload_columns_3 = standardload([deadload_columns_3], [liveload_roof, liveload_snow])โdesignload_column_3 = designload_columns_3/((frame_x_span_n) * (frame_y_span_n))standardload_column_3 = standardload_columns_3/((frame_x_span_n) * (frame_y_span_n))โprint("3ๆฅผๅๆฑ่ท่ฝฝ")display(Markdown('$$F='+str(designload_column_3)+'$$'))โ# 2ๆฅผ๏ผๆๆฃ้คไธไพง่พนๆฑ๏ผโdeadload_columns_only_2 = (column.density_perlength * frame_z_2 * (frame_x_span_n+1) * (frame_y_span_n+1)) * gโdeadload_columns_2 = deadload_columns_3 + deadload_perstory + deadload_columns_only_2 liveload_columns_2 = liveload_columns_3 + liveload_perstory designload_columns_2 = designload([deadload_columns_2], [liveload_columns_2, liveload_snow])standardload_columns_2 = standardload([deadload_columns_2], [liveload_columns_2, liveload_snow])โdesignload_column_2 = designload_columns_2/((frame_x_span_n) * (frame_y_span_n))standardload_column_2 = standardload_columns_2/((frame_x_span_n) * (frame_y_span_n))โprint("2ๆฅผๅๆฑ่ท่ฝฝ")display(Markdown('$$F='+str(designload_column_2)+'$$'))โ# 1ๆฅผ๏ผๆๆฃ้คไธไพง่พนๆฑ๏ผโdeadload_columns_only_1 = (column.density_perlength * frame_z_1 * (frame_x_span_n+1) * (frame_y_span_n+1)) * gโdeadload_columns_1 = deadload_columns_2 + deadload_perstory + deadload_columns_only_1 liveload_columns_1 = liveload_columns_2 + liveload_perstory designload_columns_1 = designload([deadload_columns_1], [liveload_columns_1, liveload_snow])standardload_columns_1 = standardload([deadload_columns_1], [liveload_columns_1, liveload_snow])โdesignload_column_1 = designload_columns_1/((frame_x_span_n) * (frame_y_span_n))standardload_column_1 = standardload_columns_1/((frame_x_span_n) * (frame_y_span_n))โprint("1ๆฅผๅๆฑ่ท่ฝฝ")display(Markdown('$$F='+str(designload_column_1)+'$$'))โxxxxxxxxxx้ฟ็ปๆฏๆ นๆฎGB0005-2017 p32 ๆ่ถๅๆจ่ฎก็ฎ้ฟ็ปๆฏๆ นๆฎGB0005-2017 p32 ๆ่ถๅๆจ่ฎก็ฎ
In [25]:
xxxxxxxxxximport numpy as npa_c = 0.91b_c = 3.69c_c = 3.45beta = 1.05E_k = 10000e6f_ck = 71.2e6โlambda_c = c_c * np.sqrt(beta*E_k/f_ck)lambda_cโdisplay(Markdown('$$\lambda_c='+str(lambda_c)+'$$'))In [26]:
xxxxxxxxxx# GB0005-2017 p32def phi(lambda_): if lambda_ > lambda_c: return a_c*np.pi**2*beta*E_k/lambda_**2/f_ck else: return 1/(1+(lambda_**2*f_ck)/(b_c*np.pi**2*beta*E_k))โ# GB0005-2017 ่กจ 5.1.5 ๆๆไธๅฉๆจกๅผk_l = 2.4โ# 1ๅฑl = k_l*frame_z_1i = np.sqrt(column.crosec_width**2/12)lambda_ = l/idisplay(Markdown('$$\phi='+str(phi(lambda_))+'$$'))โprint("็ญๆๅบๅ")display(Markdown('$$\sigma='+str(designload_column_1/phi(lambda_)/column.A)+'$$'))xxxxxxxxxxๅฐไบglubamๆๅๅผบๅบฆๅฐไบglubamๆๅๅผบๅบฆ
xxxxxxxxxx$$[\sigma]=62.9e6$$xxxxxxxxxxๆช้ขๅฎๅ
จๆช้ขๅฎๅ จ
xxxxxxxxxxไฝฟ็จ็ไฝฟ็จ็
In [27]:
xxxxxxxxxxdesignload_column_1/phi(lambda_)/column.A/71.2e6display(Markdown('$$utilization='+str(designload_column_1/phi(lambda_)/column.A/62.9e6)+'$$'))xxxxxxxxxx็ฌฆๅๅผบๆฑๅผฑๆข็ฌฆๅๅผบๆฑๅผฑๆข
xxxxxxxxxx## 4 ๅฐ้่ฎก็ฎโๆ นๆฎ GB18306-2015 ้ๅฝA 6ๅบฆๅณๅฏโๆ นๆฎ่่ๅธ ๆ7ๅบฆ่ฎพ้ฒโๆ นๆฎ GBT51226-2017 p9 4.3.4.2 ๅฏๆๅบ้จๅชๅๆณ่ฎก็ฎ4 ๅฐ้่ฎก็ฎยถ
ๆ นๆฎ GB18306-2015 ้ๅฝA 6ๅบฆๅณๅฏ
ๆ นๆฎ่่ๅธ ๆ7ๅบฆ่ฎพ้ฒ
ๆ นๆฎ GBT51226-2017 p9 4.3.4.2 ๅฏๆๅบ้จๅชๅๆณ่ฎก็ฎ
In [28]:
xxxxxxxxxxG_eq = 1 * 3 * deadload_perstory + 1 * 2 * liveload_perstory + 0.5 * liveload_snowโm_1 = (deadload_perstory + liveload_perstory)/gโm_2 = (deadload_perstory + liveload_perstory)/gโm_3 = (deadload_roof + 0.5 * liveload_snow)/gxxxxxxxxxx### 4.1 ๅบ้จๅชๅๆณโ#### 4.1.1 ๆๆกๆถ ๅๆง่็น ไธ่่ๆๆโGB5001-2010 p354 eq5.2.1 โGB5001-2010 p33 ่กจ5.1.4-1โๅค้ๅฐ้ $\alpha_1 = 0.08$ ็ฝ้ๅฐ้ $\alpha_1 = 0.50$โๅ$\alpha_1 = 0.50$In [29]:
xxxxxxxxxxalpha_1_common = 0.08alpha_1_rare = 0.5โalpha_1 = alpha_1_rareIn [30]:
xxxxxxxxxxG_eq = 0.85*(m_1+m_2+m_3)*gdisplay(Math('G_{eq} = '+str(G_eq)))In [31]:
xxxxxxxxxxF_Ek = alpha_1 * G_eqG = [m_1 * g, m_2 * g, m_3 * g]H = frame_z_abssF_1s_1 = G[0]*H[0]/np.dot(G,H)*F_Ek*(1-0)โdisplay(Math('F_{1s,1} = '+str(F_1s_1)))xxxxxxxxxx#### 4.1.2 ๆ้ฐๆฅ ่่ๆๆ๏ผ้ๅฑๆฒๆฏๆ๏ผ ่ฎก็ฎโๆฏๆโ$$0.2 \times 0.2$$โ็ปๆ็ฎๅไธบ้ๅฎๆกๆถ๏ผๆฏๆๆ่ฝดๅๆไปถ่ฎก็ฎ4.1.2 ๆ้ฐๆฅ ่่ๆๆ๏ผ้ๅฑๆฒๆฏๆ๏ผ ่ฎก็ฎยถ
ๆฏๆ
็ปๆ็ฎๅไธบ้ๅฎๆกๆถ๏ผๆฏๆๆ่ฝดๅๆไปถ่ฎก็ฎ
In [32]:
xxxxxxxxxxv_support = Beam(material_glubam, 0.2, 0.2)v_support_length = np.sqrt((frame_y_span/2)**2+(frame_z_1)**2)cos_theta = (frame_y_span/2)/v_support_lengthN = F_1s_1/4/cos_thetaโl = k_l*v_support_lengthi = np.sqrt(v_support.crosec_width**2/12)lambda_ = l/idisplay(Markdown('$$\phi='+str(phi(lambda_))+'$$'))In [33]:
xxxxxxxxxxprint("็ญๆๅบๅ")display(Markdown('$$\sigma='+str(N/phi(lambda_)/column.A)+'$$'))xxxxxxxxxxๅฐไบglubamๆๅๅผบๅบฆๅฐไบglubamๆๅๅผบๅบฆ
xxxxxxxxxx$$[\sigma] = 62.9e6$$xxxxxxxxxxๆฏๆๅฎๅ
จๆฏๆๅฎๅ จ
In [34]:
xxxxxxxxxx# GB50011-2010 p35โdef stiffness_per_column(E, I, L): return 12 * E*I/L**3โk_1 = (frame_y_span_n+1) * stiffness_per_column(material_glubam.E, column.I, frame_z_1)โk_2 = (frame_y_span_n+1) * stiffness_per_column(material_glubam.E, column.I, frame_z_2)โk_3 = (frame_y_span_n) * stiffness_per_column(material_glubam.E, column.I, frame_z_3)โm = np.array( [[m_1,0,0], [0,m_2,0], [0,0,m_3]])โk = np.array( [[k_1+k_2, -k_2, 0], [ -k_2, k_2+k_3, -k_3], [ 0, -k_3, k_3]])xxxxxxxxxx$$(\mathbf{k}-\mathbf{\omega^2} \mathbf{m}) \mathbf{\phi} = \mathbf{0}$$In [35]:
xxxxxxxxxxfrom scipy.linalg import eigh, deteigvals, eigvecs = eigh(k, m, eigvals_only=False)eigvecs_normed = eigvecs / np.linalg.norm(eigvecs, axis=0)xxxxxxxxxxๆฏๅๆฏๅ
In [36]:
xxxxxxxxxxdisplay(Math('\mathbf{\Phi} = '+latex_matrix(eigvecs)))import matplotlib.pyplot as pltplt.figure(figsize=(2, 4))plt.plot(np.append([0],eigvecs[:,0]), np.append([0],frame_z_abss),label='$\phi_1$')plt.plot(np.append([0],eigvecs[:,1]), np.append([0],frame_z_abss),label='$\phi_2$')plt.plot(np.append([0],eigvecs[:,2]), np.append([0],frame_z_abss),label='$\phi_3$')plt.legend();plt.xlabel('$\phi$');plt.ylabel('$z$');
xxxxxxxxxx$w^2$
In [37]:
xxxxxxxxxxdisplay(Math('w^2 = '+latex_matrix(eigvals)))xxxxxxxxxx่ชๆฏๅจๆ่ชๆฏๅจๆ
In [38]:
xxxxxxxxxxT = []for i, w2 in enumerate(eigvals): T.append(2*np.pi/np.sqrt(w2))display(Math('T = '+latex_matrix(T)))xxxxxxxxxx้่ฆๅบๅฐไฟกๆฏ่ฟ่กๅ็ปญ่ฎก็ฎโๆๆ$0.1g$, $T_g = 0.4$โๆ นๆฎโGB50011-2010 p34 5.1.5โGB50011-2010 p36 5.2.2โๆSRSS็ปๅ้่ฆๅบๅฐไฟกๆฏ่ฟ่กๅ็ปญ่ฎก็ฎ
ๆๆ,
ๆ นๆฎ
GB50011-2010 p34 5.1.5
GB50011-2010 p36 5.2.2
ๆSRSS็ปๅ
In [39]:
xxxxxxxxxxT_g = 0.4alpha_max = 0.5# GB50011-2010 p34 5.1.5def alpha(T, T_g, alpha_max, eta_2=1, zeta=0.05): gamma = 0.9 + (0.05-zeta)/(0.3+6*zeta) if T<0.1: alpha = (5.5*T+0.45)*eta_2*alpha_max elif T<T_g: alpha = eta_2*alpha_max elif T<5*T_g: alpha = np.power(T_g/T,gamma)*eta_2*alpha_max elif T<6: eta_1 = 0.02+(0.05-zeta)/(4+32*zeta) if eta_1<0: eta_1 = 0 alpha = np.abs(eta_2*np.power(0.2, gamma)-eta_1*(T-5*T_g))*alpha_max return(alpha)โG = np.array([m_1, m_2, m_3])*ggamma_j = (eigvecs.T@G)/((eigvecs.T*eigvecs.T)@G)โalpha_j = np.array([alpha(T[0], T_g, alpha_max), alpha(T[1], T_g, alpha_max), alpha(T[2], T_g, alpha_max)])F = eigvecs.copy()โfor j in range(len(gamma_j)): for i in range(len(G)): F[j,i] = alpha_j[j]*gamma_j[j]*eigvecs[j,i]*G[i]display(Math('F = '+latex_matrix(F)))โF_1s_2 = np.sqrt(sum(F[:,1]*F[:,1]))display(Math('F_{1s,2} = '+str(F_1s_2)))xxxxxxxxxx#### 4.2.2 ๆ้ฐๆฅ ่่ๆๆ๏ผ้ๅฑๆฒๆฏๆ๏ผ ่ฎก็ฎโๆฏๆโ$$0.3 \times 0.3$$In [40]:
xxxxxxxxxx# GB50011-2010 p35โv_support = Beam(material_glubam, 0.2, 0.2)v_support_length = np.sqrt((frame_y_span/2)**2+(frame_z_1)**2)cos_theta = (frame_y_span/2)/v_support_lengthโk_1 = 4 * material_glubam.E * v_support.A * cos_thetaโk_2 = k_1โk_3 = k_1โm = np.array( [[m_1,0,0], [0,m_2,0], [0,0,m_3]])โk = np.array( [[k_1+k_2, -k_2, 0], [ -k_2, k_2+k_3, -k_3], [ 0, -k_3, k_3]])xxxxxxxxxx$$(\mathbf{k}-\mathbf{\omega^2} \mathbf{m}) \mathbf{\phi} = \mathbf{0}$$In [41]:
xxxxxxxxxxfrom scipy.linalg import eigh, deteigvals, eigvecs = eigh(k, m, eigvals_only=False)eigvecs_normed = eigvecs / np.linalg.norm(eigvecs, axis=0)xxxxxxxxxxๆฏๅๆฏๅ
In [42]:
xxxxxxxxxxdisplay(Math('\mathbf{\Phi} = '+latex_matrix(eigvecs)))import matplotlib.pyplot as pltplt.figure(figsize=(2, 4))plt.plot(np.append([0],eigvecs[:,0]), np.append([0],frame_z_abss),label='$\phi_1$')plt.plot(np.append([0],eigvecs[:,1]), np.append([0],frame_z_abss),label='$\phi_2$')plt.plot(np.append([0],eigvecs[:,2]), np.append([0],frame_z_abss),label='$\phi_3$')plt.legend();plt.xlabel('$\phi$');plt.ylabel('$z$');
xxxxxxxxxx$w^2$
In [43]:
xxxxxxxxxxdisplay(Math('w^2 = '+latex_matrix(eigvals)))xxxxxxxxxx่ชๆฏๅจๆ่ชๆฏๅจๆ
In [44]:
xxxxxxxxxxT = []for i, w2 in enumerate(eigvals): T.append(2*np.pi/np.sqrt(w2))display(Math('T = '+latex_matrix(T)))xxxxxxxxxx้่ฆๅบๅฐไฟกๆฏ่ฟ่กๅ็ปญ่ฎก็ฎโๆๆ$0.1g$, $T_g = 0.4$โๆ นๆฎโGB50011-2010 p34 5.1.5โGB50011-2010 p36 5.2.2โๆSRSS็ปๅ้่ฆๅบๅฐไฟกๆฏ่ฟ่กๅ็ปญ่ฎก็ฎ
ๆๆ,
ๆ นๆฎ
GB50011-2010 p34 5.1.5
GB50011-2010 p36 5.2.2
ๆSRSS็ปๅ
In [45]:
xxxxxxxxxxT_g = 0.4alpha_max = 0.5# GB50011-2010 p34 5.1.5def alpha(T, T_g, alpha_max, eta_2=1, zeta=0.05): gamma = 0.9 + (0.05-zeta)/(0.3+6*zeta) if T<0.1: alpha = (5.5*T+0.45)*eta_2*alpha_max elif T<T_g: alpha = eta_2*alpha_max elif T<5*T_g: alpha = np.power(T_g/T,gamma)*eta_2*alpha_max elif T<6: eta_1 = 0.02+(0.05-zeta)/(4+32*zeta) if eta_1<0: eta_1 = 0 alpha = np.abs(eta_2*np.power(0.2, gamma)-eta_1*(T-5*T_g))*alpha_max return(alpha)โG = np.array([m_1, m_2, m_3])*ggamma_j = (eigvecs.T@G)/((eigvecs.T*eigvecs.T)@G)โalpha_j = np.array([alpha(T[0], T_g, alpha_max), alpha(T[1], T_g, alpha_max), alpha(T[2], T_g, alpha_max)])F = eigvecs.copy()โfor j in range(len(gamma_j)): for i in range(len(G)): F[j,i] = alpha_j[j]*gamma_j[j]*eigvecs[j,i]*G[i]display(Math('F = '+latex_matrix(F)))โF_1s_2 = np.sqrt(sum(F[:,1]*F[:,1]))display(Math('F_{1s,2} = '+str(F_1s_2)))xxxxxxxxxx็ปๆ็ฎๅไธบ้ๅฎๆกๆถ๏ผๆฏๆๆ่ฝดๅๆไปถ่ฎก็ฎ็ปๆ็ฎๅไธบ้ๅฎๆกๆถ๏ผๆฏๆๆ่ฝดๅๆไปถ่ฎก็ฎ
In [46]:
xxxxxxxxxxN = F_1s_2/4/cos_thetaโl = k_l*v_support_lengthi = np.sqrt(v_support.crosec_width**2/12)lambda_ = l/idisplay(Markdown('$$\phi='+str(phi(lambda_))+'$$'))In [47]:
xxxxxxxxxxprint("็ญๆๅบๅ")display(Markdown('$$\sigma='+str(N/phi(lambda_)/column.A)+'$$'))xxxxxxxxxxๅฐไบglubamๆๅๅผบๅบฆๅฐไบglubamๆๅๅผบๅบฆ
xxxxxxxxxx$$[\sigma] = 62.9e6$$xxxxxxxxxxๆฏๆๅฎๅ
จๆฏๆๅฎๅ จ
xxxxxxxxxx## 4.3 ้ช็ฎ1ๅฑๅๆฑโ1ๅฑๆปๆจชๅๅๆไธ่ฟฐๆนๆณไธญ่พๅคงๅผ4.3 ้ช็ฎ1ๅฑๅๆฑยถ
1ๅฑๆปๆจชๅๅๆไธ่ฟฐๆนๆณไธญ่พๅคงๅผ
In [48]:
xxxxxxxxxxF_1s = max(F_1s_1, F_1s_2)display(Math('F_1s = '+str(F_1s)))xxxxxxxxxxๆฑ่งฃๅๅฑ2ๆฆ่ฟ็ปญ้ขๆถ๏ผไธๅฎ้
็ปๆ็ธๆฏ่ฏฅ็ปๆ็บฆๆไธ่ถณ๏ผๆดๅ ๅฑ้ฉ๏ผๅ ๆญค่ฎก็ฎๆฏๅฎๅ
จ็๏ผ๏ผๅ
จ่็นๅบๆฅ๏ผไธ่่ไบ้ถๆๅบ๏ผๆUCB CEE220ๆฑ่งฃๅๅฑ2ๆฆ่ฟ็ปญ้ขๆถ๏ผไธๅฎ้ ็ปๆ็ธๆฏ่ฏฅ็ปๆ็บฆๆไธ่ถณ๏ผๆดๅ ๅฑ้ฉ๏ผๅ ๆญค่ฎก็ฎๆฏๅฎๅ จ็๏ผ๏ผๅ จ่็นๅบๆฅ๏ผไธ่่ไบ้ถๆๅบ๏ผๆUCB CEE220
In [49]:
xxxxxxxxxxEIc = material_glubam.E*column.IEIb = material_glubam.E*beam.ILc = frame_z_1Lb = frame_y_spank11 = 12*EIc/Lc**3 * 3k12 = -6*EIc/Lc**2k13 = k12k14 = k12k21 = k12k22 = 4*EIc/Lc + 4*EIb/Lbk23 = EIb/Lbk24 = 0k31 = k13k32 = k23k33 = 4*EIc/Lc + 8*EIb/Lbk34 = k23k41 = k14k42 = k24k43 = k34k44 = k22โK = np.array([ [k11,k12,k13,k14], [k21,k22,k23,k24], [k31,k32,k33,k34], [k41,k42,k43,k44]])*(frame_x_span_n+1)โdisplay(Math('K = '+latex_matrix(K)))โP0 = np.array([F_1s, 0,0,0])display(Math('P_0 = '+latex_matrix(P0)))Uf = np.linalg.inv(K)@P0โprint("1ๅฑๅนฟไนไฝ็งป")display(Math('U_f = '+latex_matrix(Uf)))โF_1 = Uf[0]*12*EIc/Lc**3 - Uf[2]*6*EIc/Lc**2print("1ๆฅผไธญๆฑๅชๅ")display(Math('F_1 = '+str(F_1)))โM_1 = Uf[0]*(-6)*EIc/Lc**2 + Uf[2]*2*EIc/Lcprint("1ๆฅผไธญๆฑๆฏๅบงๅผฏ็ฉ")display(Math('M_1 = '+str(M_1)))xxxxxxxxxxๆ นๆฎ GB50005-2017 p39 5.3.2 ้ช็ฎๅผบๅบฆๆ นๆฎ GB50005-2017 p39 5.3.2 ้ช็ฎๅผบๅบฆ
In [50]:
xxxxxxxxxxN = standardload_column_1A_n = column.Af_c = 71.2e6M_0 = -M_1e_0 = 0.05 * column.crosec_heightWn = column.I/(column.crosec_height/2)f_m = 84.3e6โN/A_n/f_c + (M_0+N*e_0)/Wn/f_m<1display(Math('\cfrac{N}{A_n f_c} + \cfrac{M_0+Ne_0}{Wn f_m} = '+str(N/A_n/f_c + (M_0+N*e_0)/Wn/f_m) + '<1'))โxxxxxxxxxxๆ นๆฎ GB50005-2017 p39 5.3.2 ้ช็ฎ็จณๅฎๆงๆ นๆฎ GB50005-2017 p39 5.3.2 ้ช็ฎ็จณๅฎๆง
In [51]:
xxxxxxxxxxA_0 = column.AA = column.Ak = (M_0+N*e_0)/Wn/f_m/(1+np.sqrt(N/A/f_c))display(Math('k = \cfrac{M_0+N e_0}{Wn f_m (1+\sqrt{\cfrac{N}{A f_c}})} = '+str((M_0+N*e_0)/Wn/f_m/(1+np.sqrt(N/A/f_c)))))k_0 = N*e_0/(Wn*f_m*(1+np.sqrt(N/A/f_c)))display(Math('k_0 = \cfrac{N e_0}{Wn f_m (1+\sqrt{\cfrac{N}{A f_c}})} = '+str(N*e_0/(Wn*f_m*(1+np.sqrt(N/A/f_c))))))phi_m=(1-k)**2*(1-k_0)display(Math('\phi_m=(1-k)^2 (1-k_0) = '+str((1-k)**2*(1-k_0))))N/phi(lambda_)/phi_m/A_0display(Math('\cfrac{N}{\phi \phi_m A_0} = '+str(N/phi(lambda_)/phi_m/A_0) + '< ' + str(f_c)))xxxxxxxxxxๆไปถ็จณๅฎๆไปถ็จณๅฎ
xxxxxxxxxxๆ นๆฎ GB50005-2017 p39 5.3.3 ้ช็ฎไพงๅ็จณๅฎๆง $\phi_l$ ๆ นๆฎGB50005-2017 p34 5.2.2 ๆ่ถๅๆจ่ฎก็ฎโ$f_{mk}$ ๆ นๆฎ Y. Wu, Y. Xiao, Steel and glubam hybrid space truss, Engineering Structures 171, 2018, p140 ๅ$84.3e6$ๆ นๆฎ GB50005-2017 p39 5.3.3 ้ช็ฎไพงๅ็จณๅฎๆง
ๆ นๆฎGB50005-2017 p34 5.2.2 ๆ่ถๅๆจ่ฎก็ฎ
ๆ นๆฎ Y. Wu, Y. Xiao, Steel and glubam hybrid space truss, Engineering Structures 171, 2018, p140 ๅ
In [52]:
xxxxxxxxxxl = k_l*frame_z_1i = np.sqrt(column.crosec_width**2/12)lambda_ = l/iโI_y = column.crosec_height**3*column.crosec_width/12lambda_y = l/np.sqrt(I_y / column.A)phi_y = phi(lambda_y)W = I_y/(column.crosec_width/2)โa_m = 0.7b_m = 4.9c_m = 0.9beta = 1.05E_k = 10000e6f_mk = 84.3e6lambda_m = c_m*np.sqrt(beta*E_k/f_mk)b = column.crosec_widthh = column.crosec_heightl_e = frame_z_1lambda_B = np.sqrt(l_e*h/b**2)if lambda_B>lambda_m: phi_l = a_m*beta*E_k/lambda_B**2/f_mkelse: phi_l = 1/(1+lambda_B**2*f_mk/b_m/beta/E_k)โN/phi_y/A_0/f_c + ((M_0)/phi_l/W/f_m)**2display(Math('\cfrac{N}{\phi_y A_0 f_c} + (\cfrac{M_0}{\phi_l W f_m})^2 = '+str(N/phi_y/A_0/f_c + ((M_0)/phi_l/W/f_m)**2) + '<1'))xxxxxxxxxxไพงๅ็จณๅฎไพงๅ็จณๅฎ
In [ ]:
โ