2) Determine the support reactions and draw the bending moment and the shearing force diagrams for the indeterminate beam shown in Figure EI = constant Solve by using stiffness method and Moment distribution method also 2 m B 2 m 40 kN

Flexibility Method: Beams and Frames with more than one redundant, and a Truss with one redundant. Solve the following 3 problems: Problem 1: Given: The following beam has fixed supports at A and B, and has a constant EI. W Required: Evaluate the two vertical reactions (Ay and By) and the two moment reactions (MA and MB). Neglect Ax and Bx. Draw the Shear Diagram Draw the Moment Diagram Sketch the deflected shape Hint: In this problem, it looks like it is indeterminate to the third degree, but let's neglect axial effects. By neglecting axial effects, we are not considering the horizontal force equilibrium equation (i.e., we neglect sum of fores in the x-direction). Thus, we neglect the two horizontal reactions (Ax and Bx). Therefore, the problem simplifies as follows: We are left with 2 equilibrium equations (i.e., sum of forces in the y-direction and sum of moments). So, you have 2 equations and 4 unknowns: Ay, MA, By, and MB. Thus, we need to come up with 2 more equations..these are…

Question: Determine the internal loading in the hook shown below at the point R, 8. A free body diagram of the hook's end is provided. The hook may be analysed as a 2 dimensional body. Given: R = 0.2 m 0 = 30 deg F-3 KN 1) Find the normal force N. 2) Find the shear force V. 3) Find the bending moment M. N

for the beam and loading shown  (a)use discontinnuity functions to write the expression for w(x). include the beam reactions in this expression.  (B) intergrate w(x) twice to determine v(x) and m(x). (C) Use v(x) and m(x) to plot the shear- force and bending- moment diagrams.

The beam is supported by a roller at B and a pin at C and is subjected to the distributed load shown with intensity w = 180 N/m. The maximum positive and negative internal bending moments are critical factors in the design of the beam material and geometry. Determine the largest positive and negative internal bending moments that occur in the beam and the points along the length where each occurs. Take z = 0 to be at point A at the left edge of the beam. cc 1❀0 BY NC SA 2016 Eric Davishahl a X b -a- 4.00 m 5.20 m B Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value The maximum negative internal bending moment is and occurs at z =| m to the right of A. The maximum positive internal bending moment is and occurs at x = W m to the right of A. ·b- N-m N-m

Determine the moment reactions at the supports, and then draw the shear and moment diagrams. EI is constant. Solve using Conjugate Beam Method.. Ay=?, Ma=? https://twitter.com/messages/media/1464455411780653063

Problem 2 -A concentrated couple, = 600 Nm acts at the center of the simply Supported beam which is also asted upon by the distributed load shown in the figure. Assume that the beam itself is weightless. (a) Find the internal shear Vx) and moment M(x) as a functions of x. (b) Draw the shear and moment diagrams. Label the values at x = 0, x = 6, x = 12, and at any point where V(x) or M(x) is a local maximum or minimum. y 50 N/m Mo 6 m 6 m

For the statically indeterminate beam shown in Figure 2, use the stiffness method to: (a) Determine the element stiffness matrix, k; for each element. (b) Assemble the structural stiffness matrix, K for the entire truss. (c) Determine the deflection, D and rotation, Q at joint B. (d) Determine all the reactions, Q at supports. (e) Draw the quantitative shear and bending moment diagrams. A is fixed support, B and C are roller supports. El are constant values. 20KN 4kN/m A B 1.5 m 10m 3 m Figure 2: Statically indeterminate beam

Problem 1 A simply supported prismatic beam AB carries a uniformly distributed load w per unit length. Determine: d¹y (a) Start with the EI=-w and integrate it twice to ,d²y dx4 get to El= M(x)=?. Show what? is. dx² a. Hint: What is the moment at both ends? (b) Derive the Moment equation and does it match the solution you got for (a) (c) Equation of the elastic curve in variables by integrating your solution for (a) twice more and solving for the last two constants of integration. (d) The maximum deflection of the beam in variables W Answer: (a) y = 24 (−x¹ + 2Lx² − Ľ³x) (b) \y\max 24EI B 5wL4 38EI

For the statically indeterminate beam shown in Figure 2, use the stiffness method to: (a) Determine the element stiffness matrix, k; for each element. (b) Assemble the structural stiffness matrix, K for the entire truss. (c) Determine the deflection, D and rotation, Q at joint B. (d) Determine all the reactions, Q at supports. (e) Draw the quantitative shear and bending moment diagrams. A is fixed support, B and C are roller supports. El are constant values. 20kN 4kN/m C A В 1.5 m 10m 3 m Figure 2: Statically indeterminate beam