The deflection equation of a beam is given as a polynomial y=a +bx+cx +dx The deflection...

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The deflection equation of a beam is given as a polynomial y=a +b²x+c²x² +dx² The deflection equation is to be written into its shape functions to the format and the shape functions are to be analysed y = H1*q1 + H2*q2 + H3*q3 + H4*q4 Where H# are the shape functions of a 2 noded 2D beam of length L q1 is the deflection of the left hand nodex = 0 q2 is the slope (dy/dx) of the beam at the left hand node x = 0 q3 is the deflection of the right hand node x = L q4 is the slope (dy/dx) of the beam at the right hand node x = L a) Solve the equation for a, b, c, d using the boundary conditions and write them in terms of q1, q2, q3, q4 and L. b) Substitute the values of a, b, c, d into the deflection equation and rearrange to obtain H1, H2, H3, H4. c) The shape of H2 is given as 0.2 H2(x) 0.1 0.5 Determine the maximum value and the location along L G= d) If the stress is given by the expression Myb Determine the expression for the bending moment The deflection equation of a beam is given as a polynomial y=a +b²x+c²x² +dx² The deflection equation is to be written into its shape functions to the format and the shape functions are to be analysed y = H1*q1 + H2*q2 + H3*q3 + H4*q4 Where H# are the shape functions of a 2 noded 2D beam of length L q1 is the deflection of the left hand nodex = 0 q2 is the slope (dy/dx) of the beam at the left hand node x = 0 q3 is the deflection of the right hand node x = L q4 is the slope (dy/dx) of the beam at the right hand node x = L a) Solve the equation for a, b, c, d using the boundary conditions and write them in terms of q1, q2, q3, q4 and L. b) Substitute the values of a, b, c, d into the deflection equation and rearrange to obtain H1, H2, H3, H4. c) The shape of H2 is given as 0.2 H2(x) 0.1 0.5 Determine the maximum value and the location along L G= d) If the stress is given by the expression Myb Determine the expression for the bending moment