Structural Analysis Methods II: Structural Systems - Mechanics of Structures: Variational and Computational Methods - page 319

FIGURE P5.4
Beam with multiple loadings.

5.5 Find the state variables (deflection, slope, shear force, and bending moments) along
th e beam of Fi g. P 5.5. Let L

2000 cm 4 , E 207 GN/m 2 , p 0

= 2m, I = = = 1 kN/m,

= =

P 3 kN, and M 2 kNm.

Partial Answer:

x ( m )w( mm ) θ ( rad ) V ( N ) M ( Nm )

0 0 0 800 − 183 . 3

10 − 4

1 0 0 . 1208 × 4000 − 1883 . 0

2 0 . 0644 0 3000 1617 . 0

FIGURE P5.5
Beam with guided end and in-span support.

5.6 Find the responses along the beam of Fig. P5.6.
Partial Answer:

x ( m )w( mm ) θ ( rad ) V ( N ) M ( Nm )

10 − 3 0 1 . 1470 0 . 2523 × 0 0

10 − 3

5 0 0 . 1608 × 5067 − 37 500

10 − 4

11 − 0 . 2305 − 0 . 4823 × 67 . 34 − 13 100

10 − 3

14 0 − 0 . 1053 × 20 680 − 12 890

24 0 0 − 29 320 − 56 050