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Homework answers / question archive / Finite Element Method Problem statement(s): A truss bridge is a type of bridge with medium spans

Finite Element Method

Problem statement(s): A truss bridge is a type of bridge with medium spans. The bridge derives its load-bearing power to a truss, a generally steel structure on both sides of the bridge deck, which is made up of triangular parts (see Figure 1). Triangles retain their shape, and offer the construction therefore has the required sturdiness. Depending on the position in the construction steps there are both tensile and compressive forces on the construction parts.

The specific concept of trusses ensures that there is no (or little) bending moment in the bars/beams.

• Model and analyze the steel train bridge (from Figure 1) incl. (stationary) train load.

Targets:

• Being able to make manual control and computer calculations regarding:

o Powers

o Movements

o Tensions

o Control of plastic behaviour:

? Safety factor (in relation to yield stress)

o Bonus: Check for kink hazard (Eulerknik)

Inside information: Parts 1 and parts 2.1 and 2.2 (special part 2.1)

Problem statement(s):

• Analyze the simplified (modelled) truss bridge (Figure 1).

Figure 1: “Loaded train (truss) bridge”

Si units:

Dimensions in meters (m)

Load in newtons (N)

Rod A

60° 60°

3.6

280k 210k 280k 360k

3.6 3.6

Additional construction data:

e Rod (Link) data:

o Effective area is 3250 mm” (Section data: Link area) = 0.00325 m?

o Material properties:

" (0 2 = flow limit = E235 (= 2.35x10° N/m')

= E-=elasticity modulus = 2.0E11 (N/m7) .... Or.... 200 GPa

=" v = transverse contraction = 0.3

nodes

Pp 2 4 6

JVV\

z, 3 5

4

Figure 2a: “Example junction numbering train (truss) bridge”'

element number

L4 L8

BarA=L1/ 13\ 1s/ 7\ 19 / Lu

L2 L6 L10

at

a" a

Figure 2b: “Example Element numbering train (truss) bridge”

Tool : Table |

Create from Figure | and 2 a node (keypoint) table (see Table 1).

Table 1: Junctions associated with loaded train bridge (Figure 1).

† Key point | x(m)—— | vm)

© NLDA-MS&T 3

? NLDA-MS&T 4

Exercises

Task 1

Sketch the course of the expected deformation. (Without using Ansys as an aid)

Make an Ansys plot (+ save) of the total sag . Does this match?

Exercise 2

Calculate reaction forces by hand.

Compare this with Ansys (List/Results/Reaction solution). conclusion ?

Assignment 3

Calculate by hand for bar A (see Figure 1) the bar force and (bar) tension.

What value does Ansys give for the force (SMISC,1) and stress (LS,1) in this member A ?

conclusion ?

Assignment 4

Which bars (in Figure 3) are loaded under compression and which are loaded under tension (indicated in Figure 3)?

(Without using Ansys as an aid)

Create an Ansys tension plot

(Tip: Element Table + LS,1 ….Plot Elem Table …+ save). Does this match?

Are there also bars that are hardly loaded?

Assignment 5

Calculate the static safety factor(s) and indicate which bar is decisive (= lowest

safety factor, highest voltage) or whether another material should be selected.

(Use Ansys as control means, eg List Elem Table + LS,1 (= axial stress), see also Part 2-2.1 p. 10))

Figure 3: "Push/pull rods train (truss) bridge"

Assignment 6

a) What do you expect to happen when elements L2, L6 and L10 are replaced through round beam elements (Beam-188, R = 0.03217 m ? A= 0.00325 m2

†

b) Make both a displacement plot with the bridge consisting only of bars (#1) and a displacement plot with the beam 2, 6 and 10 (#2) modeled as beams.

What are the differences with your expectation (question 6a)?

c) Compare the maximum sag and maximum tension of the situation bridge made of bars and the bridge situation “rods and 3 girders”. conclusion.

Assignment 7

See question 6 (a/mc), but then replace all bars with (round) bars.