For the beam below with fixed-fixed boundary conditions, do the following calculations by hand.

Let k₁ = 480 #/in, k₂ = 310 #/in, k3 = 70 #/in, k4 = 90 #/in, k5 = 10 #/in, F₂ = 200 # and

F3 = 500 #.

1. Solve for the displacements at nodes 1 through 4 (U₁, U₂, U3, and 4).

2. Solve for the reaction forces at both ends (R₁ and R4).

R

1

F

2

TR

ка

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42

3

K3

k

3 4. 4

3 mm

K5

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43

R

4