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

T

www

F

2

2

кг

www

42

F

3

3

K3

k

4. 4

mi

K5

из

R

4

4