Question

For the beam elements shown (Node 1 is fixed and node 3 is a pin);
the nodal displacements have been calculated in meters and radians as:

V. V2 -0.001 V. 0.004 Let l 0.0001 m. and E 70 109 Nm: Neglecting the axial stiffness of the beam and using the interctions of a two-node beam element. (a) Find an equation for the slope of the beam in terms of the given nodal displacements and plot the slope diagram. (b) Find an equation for the moment of the beam in terms of the given nodal displacements and plot the moment diagram. (c) Find the maxinum bending stress (at the fixed support) using finite element. 2 m 0.15 m 4 m Beam cross-section

Answer 1

Where M? is moment at fixed End I = 0.0001 m^4 E = 70 times 10^9 N/m^2 Using Mohr�s first theorem theta_B - theta_A = Area of BMD b/w A & B/EI theta_B - theta_A = []1/3 times wl^2/8 times 1/4 l + n[2[2/3 times 3/8l times 9/128 wl^2]]/EI theta_B - theta_A = (1/96 wl^3) + (9/256 wl^3)/EI theta_B - theta_A = 35 wl^3/768 EI = 0.0453 wl^3/EI theta_B = 0.0456 wl^3/EI theta_B = 0.0456 times wl^3/0.0004 times 70 times 10^9 = 651 times 10^-9 �theta_A� is zero because there is no deflection at find end. After some length �x� the deflection starts \r\n delta_1 = wl^4/8EI delta_R = R_b l^3/3EI delta_L = delta_R = wl^4/8EI = R_b l^3/3EI = R_b = 3wl/8 (1) wl - 3/8 wl 5/8 wl = R_a (3) -M? -3/8 wl - l + wl^2/2 = 0 -M? = 3wl^2/8 -wl^2/2 -M? = 3wl^2 - 4wl^2./8 M? = wl^2/8 \r\n