In theory, Prim's MST method might be used to a realistic weighted network.

2. A uniform, simply supported beam, is loaded as shown in Figure 2. Using singularity functions, determine an expression for the bending moment at any point along the beam. Hence, determine the slope of the beam at point, A, and the deflection of the beam at point, B. The bending stiffness of the beam is 3200 Nm². 320 N 200 N/m 1.2m 0.6m Figure 2 2 A 0.4m X * B D

**DFQ** If you know statics, it helps in understanding. A uniform beam (Constant EI) with Length = L has both ends fixed. Applied loading is a uniformly varying load, zero at the left end, W at the right end. Units of the load are pounds per foot. Your results will be stated in terms of W, L, EI.You will use Laplace Transforms to solve for the beam deflection expression.  Other quantities to be determined from the deflections will use derivatives. Your results will be stated in terms of W, L, EI. (Triangular shaped distributed load) A uniform beam (Constant EI) with Length = L has both ends fixed. Applied loading is a uniformly varying load, zero at the left end, W at the right end. Units of the load are pounds per foot. A) Find the expression for deflection at any point, with x measured from the left end.

The uniaxial bar finite element equation can be used for other types of engineering problems, if proper analogy is applied. For example, consider the piping network shown in the figure. Each section of the network can be modeled using a finite element. If the flow is laminar and steady, we can write the equations for a single pipe element as: - q₁ = K(P; — P;) qi q;= K(P; - P;) qj where q; and q; are fluid flow at nodes i and j, respectively; P; and P; are fluid pressure at nodes i and j, respectively; and K is K = πD4 128μL where D is the diameter of the piper, μ is the viscosity, and L is the length of the pipe. The fluid flow is considered positive away from the node. The viscosity of the fluid is 9×104 Pa's. a. Write the element matrix equation for the flow in the pipe element. b. The net flow rates into nodes 1 and 2 are 10 and 15 m³/s, respectively. The pressures at the nodes 6, 7, and 8 are all zero. The net flow rate into the nodes 3, 4, and 5 are all zero. What is the outflow…