Suspension bridges - Computational Analysis and Design of Bridge Structures - page 380

The vertical displacement d at node B under external load P can be
derived from geometric consistency.

L
EAH P

3

d = (12.3)

2

2

The solution of displacement by geometric consistency can be improved
by the principle of minimum total potential energy, which can be simply
described as that the change of total strain energy equals the work done by
external loads or the total energy does not change. For the case shown in
Figure 12.10, it can be described as

( U V 0 )

δ Π = δ + = (12.4)

where:
Π is the total energy
U ( / ) σε is the total strain energy (internal energy)

V = − dP is the total potential energy (external work)
σ and ε are stress and strain, respectively, and linear elastic is assumed

= 2 AL 1 2

Figure 12.11 shows the stress and strain relationship and the density of
strain energy.

σ = E ε (12.5)

From geometric consistency at node B as shown in Figure 12.10, the strain
of truss elements is

σ

σ

ε

ε

0

Figure 12.11 Density of strain energy.