xxxxxxxxxx# 办公楼程序化计算书马克本计算书编写之初仅用于内部快速试算、设计、验算之用，未曾考虑公示甲方之用。虽应要求增加Latex公式行便于阅读，如仍有不便还请谅解。除非额外标注，本计算书使用国际标准单位SI。本计算书已经过SAP2000验算，结果见附。办公楼程序化计算书¶
马克
本计算书编写之初仅用于内部快速试算、设计、验算之用，未曾考虑公示甲方之用。虽应要求增加Latex公式行便于阅读，如仍有不便还请谅解。
除非额外标注，本计算书使用国际标准单位SI。
本计算书已经过SAP2000验算，结果见附。
In [1]:
xxxxxxxxxxfrom IPython.display import display, Markdown, Latex, Math# 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}'%datafrom IPython.core.display import HTMLHTML("""<style>div.output_latex { text-align: center;}.jp-OutputArea-output.jp-RenderedLatex { text-align: center;}div.output_area .MathJax_Display { text-align: center !important;}div.jp-InputArea { display: none;}</style>""")Out[1]:
xxxxxxxxxx## 1 框架布置主梁 x方向 5m x 6跨 = 30m主梁 y方向 8m x 2跨 = 16m次梁 x方向 1.6m x 5跨每榀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_spanframe_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 荷载计算### 2.1 活荷载#### 2.1.1 办公楼面活荷载根据GB50009-2012 p14$$2kN/m^2$$$$\psi_c = 0.7$$$$\psi_f = 0.5$$$$\psi_q = 0.4$$#### 2.1.2 不上人屋面活荷载根据GB50009-2012 p18$$0.5kN/m^2$$$$\psi_c = 0.7$$$$\psi_f = 0.5$$$$\psi_q = 0$$#### 2.1.3 雪荷载[雪荷载分区](https://www.dlubal.com/zh/solutions/online-services/load-zones)根据GB50009-2012 p26$$s_0 = 0.5kN/m^2$$$$\mu_r = 1$$$$s_k = \mu_r s_0 = 0.5kN/m^2$$In [3]:
xxxxxxxxxxliveload_floor_perarea = 2000liveload_roof_perarea = 500liveload_snow_perarea = 500xxxxxxxxxx### 2.2 恒荷载#### 2.2.1 轻质混凝土楼板单向板 100厚轻质混凝土根据[某公司数据](http://www.yzjz169.com/news/hydt/308.html)，保守设计取值850 kg/m3,即85kg/m2，按安全取1.2e3kg/m3 - 肖由[蒸压加气混凝土楼板(alc楼板)](https://www.hnalcb.cn/cp/e/57.html)，1.6m跨长承载力5kN/m220厚水泥砂浆找平 2e3kg/m3，即40kg/m210厚地砖2.5e3kg/m3，即25kg/m2或木地板10kg/m2总质量按较大值2.2 恒荷载¶
2.2.1 轻质混凝土楼板¶
单向板 100厚轻质混凝土根据某公司数据，保守设计取值850 kg/m3,即85kg/m2，按安全取1.2e3kg/m3 - 肖
由蒸压加气混凝土楼板(alc楼板)，1.6m跨长承载力5kN/m2
20厚水泥砂浆找平 2e3kg/m3，即40kg/m2 10厚地砖2.5e3kg/m3，即25kg/m2 或木地板10kg/m2
总质量按较大值
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 * thicknessxxxxxxxxxx经计算，每平方米质量经计算，每平方米质量
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)mass_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 /12beam_sub = Beam(material_glubam, 0.12, 0.36)beam = Beam(material_glubam, 0.3, 0.6)column = Beam(material_glubam, 0.3, 0.5)xxxxxxxxxx根据GB50009-2012 3.2.4荷载设计值$$S_d = \max(1.2\sum{G}+1.4\sum{Q}, 1.35\sum{G}+1.4\times0.7Q)$$荷载标准值$$S_s = \sum{G}+Q_1+0.7\sum{Q_i}, (i>1)$$根据GB50009-2012 3.2.4
荷载设计值
荷载标准值
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)In [10]:
xxxxxxxxxxdeadload_floor_perarea = mass_floor_perarea * gdesignload_floor_perarea = designload([deadload_floor_perarea], [liveload_floor_perarea])designload_floor_perareadisplay(Markdown('$$S_d='+str(designload_floor_perarea)+'$$'))xxxxxxxxxx小于5kN小于5kN
xxxxxxxxxx使用率使用率
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 验算承载力$$\sigma=\cfrac{My}{I}<[\sigma]$$其中$$M = \cfrac{qL^2}{8}$$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('$$\sigma='+str(max_sigma_beam_sub)+'$$'))xxxxxxxxxx小于glubam抗拉强度按 Y. Wu, Y. Xiao, Steel and glubam hybrid space truss, Engineering Structures 171, 2018, p140, 其他材料力学性质同$$[\sigma] = 1.06e8$$小于glubam抗拉强度
按 Y. Wu, Y. Xiao, Steel and glubam hybrid space truss, Engineering Structures 171, 2018, p140, 其他材料力学性质同
xxxxxxxxxx使用率使用率
In [14]:
xxxxxxxxxxmax_sigma_beam_sub/1.06e8display(Markdown('$$utilization='+str(max_sigma_beam_sub/1.06e8)+'$$'))xxxxxxxxxx#### 3.2.2 验算正常使用极限状态位移$$u = \cfrac{5qL^4}{384EI}< [u] = \cfrac{1}{250}L$$In [15]:
xxxxxxxxxxstandardload_beam_sub_perlength = standardload([deadload_beam_sub_perlength], [liveload_beam_sub_perlength])def disp_distributed_load(q,L,E,I): return 5*q*L**4/384/E/Imax_disp_beam_sub = disp_distributed_load(standardload_beam_sub_perlength, frame_x_span, material_glubam.E, beam_sub.I)max_disp_beam_subdisplay(Markdown('$$u='+str(max_disp_beam_sub)+'$$'))xxxxxxxxxx小于限值小于限值
In [16]:
xxxxxxxxxxframe_x_span/250display(Markdown('$$[u]='+str(frame_x_span/250)+'$$'))xxxxxxxxxx使用率使用率
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('$$\sigma='+str(max_sigma_beam)+'$$'))xxxxxxxxxx小于glubam抗拉强度$$[\sigma] = 65.3e6$$小于glubam抗拉强度
xxxxxxxxxx使用率使用率
In [20]:
xxxxxxxxxxmax_sigma_beam/65.3e6display(Markdown('$$utilization='+str(max_sigma_beam/65.3e6)+'$$'))In [21]:
xxxxxxxxxxstandardload_beam_perlength = standardload([deadload_beam_perlength], [liveload_beam_perlength])def disp_distributed_load(q,L,E,I): return 5*q*L**4/384/E/Imax_disp_beam = disp_distributed_load(standardload_beam_perlength, frame_y_span, material_glubam.E, beam.I)max_disp_beamdisplay(Markdown('$$u='+str(max_disp_beam)+'$$'))xxxxxxxxxx小于限值小于限值
In [22]:
xxxxxxxxxxframe_y_span/250display(Markdown('$$u='+str(frame_y_span/250)+'$$'))xxxxxxxxxx使用率使用率
In [23]:
xxxxxxxxxxmax_disp_beam / (frame_y_span/250)display(Markdown('$$utilization='+str(max_disp_beam / (frame_y_span/250))+'$$'))xxxxxxxxxx### 3.4 柱2楼、3楼、屋面按楼面恒载，2楼、3楼按办公楼活载，屋面按雪荷载各层柱荷载如下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))*gdeadload_roof_perarea = 500deadload_roof = deadload_roof_perarea * frame_x * frame_yliveload_perstory = liveload_floor_perarea * frame_x * frame_yliveload_snow = liveload_snow_perarea * frame_x * frame_yliveload_roof = liveload_roof_perarea * frame_x * frame_y# 3楼 (按扣除一侧边柱)deadload_columns_only_3 = (column.density_perlength * frame_z_3 * (frame_x_span_n+1) * (frame_y_span_n+1)) * gdeadload_columns_3 = deadload_roof + deadload_columns_only_3liveload_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])designload_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))print("3楼单柱荷载")display(Markdown('$$F='+str(designload_column_3)+'$$'))# 2楼（按扣除一侧边柱）deadload_columns_only_2 = (column.density_perlength * frame_z_2 * (frame_x_span_n+1) * (frame_y_span_n+1)) * gdeadload_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])designload_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))print("2楼单柱荷载")display(Markdown('$$F='+str(designload_column_2)+'$$'))# 1楼（按扣除一侧边柱）deadload_columns_only_1 = (column.density_perlength * frame_z_1 * (frame_x_span_n+1) * (frame_y_span_n+1)) * gdeadload_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])designload_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))print("1楼单柱荷载")display(Markdown('$$F='+str(designload_column_1)+'$$'))xxxxxxxxxx长细比根据GB0005-2017 p32 按胶合木计算长细比根据GB0005-2017 p32 按胶合木计算
In [25]:
xxxxxxxxxximport numpy as npa_c = 0.91b_c = 3.69c_c = 3.45beta = 1.05E_k = 10000e6f_ck = 71.2e6lambda_c = c_c * np.sqrt(beta*E_k/f_ck)lambda_cdisplay(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))# GB0005-2017 表 5.1.5 按最不利模式k_l = 2.4# 1层l = k_l*frame_z_1i = np.sqrt(column.crosec_width**2/12)lambda_ = l/idisplay(Markdown('$$\phi='+str(phi(lambda_))+'$$'))print("等效应力")display(Markdown('$$\sigma='+str(designload_column_1/phi(lambda_)/column.A)+'$$'))xxxxxxxxxx小于glubam抗压强度小于glubam抗压强度
xxxxxxxxxx$$[\sigma]=62.9e6$$xxxxxxxxxx截面安全截面安全
xxxxxxxxxx使用率使用率
In [27]:
xxxxxxxxxxdesignload_column_1/phi(lambda_)/column.A/71.2e6display(Markdown('$$utilization='+str(designload_column_1/phi(lambda_)/column.A/62.9e6)+'$$'))xxxxxxxxxx符合强柱弱梁符合强柱弱梁
xxxxxxxxxx## 4 地震计算根据 GB18306-2015 附录A 6度即可根据肖老师 按7度设防根据 GBT51226-2017 p9 4.3.4.2 可按底部剪力法计算In [28]:
xxxxxxxxxxG_eq = 1 * 3 * deadload_perstory + 1 * 2 * liveload_perstory + 0.5 * liveload_snowm_1 = (deadload_perstory + liveload_perstory)/gm_2 = (deadload_perstory + liveload_perstory)/gm_3 = (deadload_roof + 0.5 * liveload_snow)/gIn [29]:
xxxxxxxxxxalpha_1_common = 0.08alpha_1_rare = 0.5alpha_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)display(Math('F_{1s,1} = '+str(F_1s_1)))xxxxxxxxxx#### 4.1.2 按铰接 考虑斜撑（非屈曲支撑） 计算支撑$$0.2 \times 0.2$$结构简化为静定桁架，支撑按轴压杆件计算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_thetal = k_l*v_support_lengthi = np.sqrt(v_support.crosec_width**2/12)lambda_ = l/idisplay(Markdown('$$\phi='+str(phi(lambda_))+'$$'))In [33]:
xxxxxxxxxxprint("等效应力")display(Markdown('$$\sigma='+str(N/phi(lambda_)/column.A)+'$$'))xxxxxxxxxx小于glubam抗压强度小于glubam抗压强度
xxxxxxxxxx$$[\sigma] = 62.9e6$$xxxxxxxxxx支撑安全支撑安全
In [34]:
xxxxxxxxxx# GB50011-2010 p35def stiffness_per_column(E, I, L): return 12 * E*I/L**3k_1 = (frame_y_span_n+1) * stiffness_per_column(material_glubam.E, column.I, frame_z_1)k_2 = (frame_y_span_n+1) * stiffness_per_column(material_glubam.E, column.I, frame_z_2)k_3 = (frame_y_span_n) * stiffness_per_column(material_glubam.E, column.I, frame_z_3)m = np.array( [[m_1,0,0], [0,m_2,0], [0,0,m_3]])k = 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)xxxxxxxxxx振型振型
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)))xxxxxxxxxx自振周期自振周期
In [38]:
xxxxxxxxxxT = []for i, w2 in enumerate(eigvals): T.append(2*np.pi/np.sqrt(w2))display(Math('T = '+latex_matrix(T)))xxxxxxxxxx需要场地信息进行后续计算暂按$0.1g$, $T_g = 0.4$根据GB50011-2010 p34 5.1.5GB50011-2010 p36 5.2.2按SRSS组合需要场地信息进行后续计算
暂按,
根据
GB50011-2010 p34 5.1.5
GB50011-2010 p36 5.2.2
按SRSS组合
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)G = np.array([m_1, m_2, m_3])*ggamma_j = (eigvecs.T@G)/((eigvecs.T*eigvecs.T)@G)alpha_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()for 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)))F_1s_2 = np.sqrt(sum(F[:,1]*F[:,1]))display(Math('F_{1s,2} = '+str(F_1s_2)))In [40]:
xxxxxxxxxx# GB50011-2010 p35v_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_lengthk_1 = 4 * material_glubam.E * v_support.A * cos_thetak_2 = k_1k_3 = k_1m = np.array( [[m_1,0,0], [0,m_2,0], [0,0,m_3]])k = 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)xxxxxxxxxx振型振型
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)))xxxxxxxxxx自振周期自振周期
In [44]:
xxxxxxxxxxT = []for i, w2 in enumerate(eigvals): T.append(2*np.pi/np.sqrt(w2))display(Math('T = '+latex_matrix(T)))xxxxxxxxxx需要场地信息进行后续计算暂按$0.1g$, $T_g = 0.4$根据GB50011-2010 p34 5.1.5GB50011-2010 p36 5.2.2按SRSS组合需要场地信息进行后续计算
暂按,
根据
GB50011-2010 p34 5.1.5
GB50011-2010 p36 5.2.2
按SRSS组合
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)G = np.array([m_1, m_2, m_3])*ggamma_j = (eigvecs.T@G)/((eigvecs.T*eigvecs.T)@G)alpha_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()for 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)))F_1s_2 = np.sqrt(sum(F[:,1]*F[:,1]))display(Math('F_{1s,2} = '+str(F_1s_2)))xxxxxxxxxx结构简化为静定桁架，支撑按轴压杆件计算结构简化为静定桁架，支撑按轴压杆件计算
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xxxxxxxxxxN = F_1s_2/4/cos_thetal = k_l*v_support_lengthi = np.sqrt(v_support.crosec_width**2/12)lambda_ = l/idisplay(Markdown('$$\phi='+str(phi(lambda_))+'$$'))In [47]:
xxxxxxxxxxprint("等效应力")display(Markdown('$$\sigma='+str(N/phi(lambda_)/column.A)+'$$'))xxxxxxxxxx小于glubam抗压强度小于glubam抗压强度
xxxxxxxxxx$$[\sigma] = 62.9e6$$xxxxxxxxxx支撑安全支撑安全
In [48]:
xxxxxxxxxxF_1s = max(F_1s_1, F_1s_2)display(Math('F_1s = '+str(F_1s)))xxxxxxxxxx求解单层2榀连续钢架（与实际结构相比该结构约束不足，更加危险，因此计算是安全的），全节点固接，不考虑二阶效应，按UCB CEE220求解单层2榀连续钢架（与实际结构相比该结构约束不足，更加危险，因此计算是安全的），全节点固接，不考虑二阶效应，按UCB CEE220
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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 = k22K = np.array([ [k11,k12,k13,k14], [k21,k22,k23,k24], [k31,k32,k33,k34], [k41,k42,k43,k44]])*(frame_x_span_n+1)display(Math('K = '+latex_matrix(K)))P0 = np.array([F_1s, 0,0,0])display(Math('P_0 = '+latex_matrix(P0)))Uf = np.linalg.inv(K)@P0print("1层广义位移")display(Math('U_f = '+latex_matrix(Uf)))F_1 = Uf[0]*12*EIc/Lc**3 - Uf[2]*6*EIc/Lc**2print("1楼中柱剪力")display(Math('F_1 = '+str(F_1)))M_1 = Uf[0]*(-6)*EIc/Lc**2 + Uf[2]*2*EIc/Lcprint("1楼中柱支座弯矩")display(Math('M_1 = '+str(M_1)))xxxxxxxxxx根据 GB50005-2017 p39 5.3.2 验算强度根据 GB50005-2017 p39 5.3.2 验算强度
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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 = 84.3e6N/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'))xxxxxxxxxx根据 GB50005-2017 p39 5.3.2 验算稳定性根据 GB50005-2017 p39 5.3.2 验算稳定性
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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)))xxxxxxxxxx杆件稳定杆件稳定
xxxxxxxxxx根据 GB50005-2017 p39 5.3.3 验算侧向稳定性 $\phi_l$ 根据GB50005-2017 p34 5.2.2 按胶合木计算$f_{mk}$ 根据 Y. Wu, Y. Xiao, Steel and glubam hybrid space truss, Engineering Structures 171, 2018, p140 取$84.3e6$根据 GB50005-2017 p39 5.3.3 验算侧向稳定性
根据GB50005-2017 p34 5.2.2 按胶合木计算
根据 Y. Wu, Y. Xiao, Steel and glubam hybrid space truss, Engineering Structures 171, 2018, p140 取
In [52]:
xxxxxxxxxxl = k_l*frame_z_1i = np.sqrt(column.crosec_width**2/12)lambda_ = l/iI_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)a_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)N/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'))xxxxxxxxxx侧向稳定侧向稳定
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