Diameter = d = Diameter = 20 Length = L Length = L The beam is fixed at both ends and pinned at the midpoint location shown above. Young's Modulus = 2 x 10^10 N/m^2 Mass Density p = 15,000 kg/m^3 Natural Frequency Wn = 3,000 rad/s Moment at midpoint of beam M = 100 N-m, which produces 15 degrees of rotation Find diameter d and length l of the circular cross sections using finite element modeling and two degrees of freedom per node
Answers
Answer:
The two-segment beam in the figure below is fixed at the ends and pinned at its midpoint. The beam is constructed of a material with Young's modulus E = 2 x 10' N/m and mass density p= 7800 kg/m°. The natural frequency of this beam is on = 1500 rad/s. A moment M = 100 N-m that is applied at the pinned midpoint and perpendicular to the figure plane produces a rotation e = 5° (degrees) at the same point. Using analytical finite element modeling and beam elements with two degrees of freedom per node, calculate the length / and the diameter d that defines the two circular cross-sections. Diameter d Diameter 2d
The beam is fixed at both ends and pinned at the midpoint location shown above.
2 x 1010 N/m2 Young's Modulus
Mass Density p = 15,000 kg/m^3
Natural Frequency Wn = 3,000 rad/s
Moment at midpoint of beam M = 100 N-m, which produces 15 degrees of rotation
Find diameter d and length l of the circular cross sections using finite element modeling and two degrees of freedom per node.
Explanation: