Comprehensive+beam+problem

# Comprehensive+beam+problem - Lecture8_problem.nb...

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Calculations for the problem worked out in lacture 8 In[1]:= Clear @ x D In[2]:= Clear @ y D Definition of loads and geometry In[3]:= Sy = - 1000 Out[3]= - 1000 In[4]:= h = 0.1 Out[4]= 0.1 In[5]:= t = 0.003 Out[5]= 0.003 In[6]:= Mx = 500 Out[6]= 500 Coordinates of the centroids of the two rectangular areas referred to the global centroidal reference system In[7]:= xc1 = - h ê 8 Out[7]= - 0.0125 In[8]:= yc1 = h ê 4 Out[8]= 0.025 In[9]:= xc2 = h ê 8 Out[9]= 0.0125 In[10]:= yc2 = - h ê 4 Out[10]= - 0.025 Moments of inertia with respect to the centroidal axes In[11]:= Ixx = h * t * yc1^2 + H 1 ê 12 L * t * h^3 + h * t * yc2^2 Out[11]= 6.25 μ 10 - 7 In[12]:= Iyy = H 1 ê 12 L * t * h^3 + h * t * xc1^2 + h * t * xc2^2 Out[12]= 3.4375 μ 10 - 7 Lecture8_problem.nb 1

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In[13]:= Ixy = h * t * xc1 * yc1 + h * t * xc2 * yc2 Out[13]= - 1.875 μ 10 - 7 Calculation of the normal stress distribution In[14]:= sigmaz = - H Mx * Ixy ê H Ixx * Iyy - Ixy^2 LL * x + H Mx * Iyy ê H Ixx * Iyy - Ixy^2 LL * y Out[14]= 5.21739 μ 10 8 x + 9.56522 μ 10 8 y ü Maximum tensile and compressive stress In[15]:= maxtensile = sigmaz ê . 8 x Ø 3h ê 8,y Ø h ê 4 < Out[15]= 4.34783 μ 10 7 In[16]:= maxcompressive = sigmaz ê . 8 x Ø h ê 8, y Ø - 3h ê 4 < Out[16]= - 6.52174 μ 10 7
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