# Truss Bridge Report

Urbain et civil

29 nov. 2013 (il y a 5 années et 1 mois)

133 vue(s)

Truss Bridge Report

Charlotte Simpson

The Truss
Bridge

What is a Truss Structure?

A structure built using singular
members connected at joints can generally be considered truss.

The designs of truss structures eliminate torsion

and shear forces
, these structures
are put under two stresses;
pure
compression and tension
.

Compression

A ‘squashing’ force, this force acts to shorten
each

member it’s acting upon.

Tension

A ‘pulling’ force,

this forces acts to lengthen each

member it’s acting upon.

For a bridge to be considered statically indeterminate they must satisfy the formula: M
>

2J
-
r

(where m = number of members, J = number of joins, r = 3)

This ensures should some members break the bridge
remains structurally sound.

The
Design
Process

Initi
al Research > Sketches & Discussion > Sketch Models > Sketches & Discussion > Final Model

Preliminary

Research

Truss bridges make efficient use of materials and are an economical alternative to earlier designed beam
bridges. There’s a huge variation betw
een each truss bridge; the truss structure itself can vary as can the
plane this is applied to. T
he height of the deck in relation to the bridge can
also
a
lter

dependent upon the
design.

Deck Truss

Te捫c楳⁡瑴慣aeT 瑯⁡nT⁬楥s⁡bove⁴he⁴牵ss⸠
No瑨楮朠
s瑲W捴c牡氠睩汬⁢e founT⁡bove⁴he⁤e捫c

Through Truss

Te捫c瑲Wvels be瑷Wen⁡nT⁴h牯u杨⁴he⁴牵ss⸠

Truss Bridge Report

Charlotte Simpson

Existing Truss Examples

The Pratt Truss

The Howe Truss

The Warren Truss

Cardboard

Why use Cardboard as a Building Material?

Car
environmentally

friendly; this material is easily recycled and provided via a
renewable source.

Existing Structures

Designing the Bridge

Half Through Truss

similar to the through tru
ss structural elements
can be found above and below the roadbed, however here the exposed
truss above the roadbed isn’t attached to the deck.

This bridge makes use of diagonal and vertical
members. The diagonal members underg
o tension
and the vertical compression; these members are
angled downwards towards

the central vertical
member.

The diagonal members are angled upwards
towards the central vertical member. These
members undergo compression whilst tension acts
upon the vertical components.

Compression and tension forces are spread
between the diagonal and vertical members
alternatively. Should a load be distributed evenly
along the surface of this structure the two
end
verticals

would have no forces acting upon them
.

Cardboard has a strong structure, especially corrugated cardboard. A thinner
sheet of bent card is sandwiched between two thicker sheets, this creates
strong and durable columns

should you apply a load through t
he columns
as oppose to across
.

Shigeru Ban uses
cardboard columns within
both structures. These
columns provides support
but also create elegant
spaces.

Left:

Biennale Pavilion
, Japan

Right:

Temporary Log Houses
,
Japan

Truss Bridge Report

Charlotte Simpson

Joining Techniques & Implications

Joints within truss structures are rigid and often referred to as nodes. It’s thought that external forces act only
at these points, forces are then transferred through the structure along individual members, either under pu
re
tension or pure compression.

It’s essential the joints are as strong as the members used within the truss.

Before designing the bridge we focused upon jointing techniques. Steel structures use bolts, the majority of
nodes

are rigid. We tested three separate joining materials before
completing our final bridge; we used a glue
gun, masking tape and multipurpose glue.

All Purpose Glue

Glue Gun

Straight cut & Angled Joints

Making the Final Design

As a group we decided to combine both a curved arch bridge and typical warren truss design for use as our
final design.

The curved arch would allow for applied forces to disperse evenly throughout the structure. The warren truss
would be built narrow, sho
rtening the member lengths and increasing their frequency throughout the
structure creates

smaller triangles and increased strength and stability

within the entirety of the structure
. The
arch and warren truss will be built separately and then attached to
one
another;

the two should join at point
s
close to the foundation pads ensuring dispersion of force through the arch into the sturdier base of the warren
truss.

The all purpose glue was easily applied to the
straws. The glue took a while to become tacky,
within which the straws had repositioned
themselves.
Once dry however
joints are very
strong

and somewhat elastic.

Masking tape achieves results similar in
accuracy to the previous glue tested. Masking
taped joints aren’t very strong and are easily
b牯步k⸠Th楳⁪o楮瑩W朠ge捨n楱ue⁩ ⁡⁳灥eTy
one⸠†

Th楳⁧汵e⁤物rsⁱu楣歬i⁡nT⁯ffe牳⁧ e慴⁳瑲 n杴g⸠
Jo楮瑳⁣ n⁢e⁰os楴楯neT⁡捣畲慴e汹⁳桯u汤⁡
Tes楧渠f楲s瑬W
be⁤牡wn⁯u琠瑯⁳ 慬攠anT⁳瑲 w
members

p污捥T⁤楲i捴汹⁯ver⁴he⁳步瑣WeT

nes
⸠Th楳 subs瑡n捥⁯ffers⁡c捵牡捹,⁳灥 T⁡nT
s瑲敮杴geneT⁪o楮瑳⸠

w慳⁢e楮朠gu琠on⁴he⁪o楮楮朠g
aterial’s strength and more on the
bridge’s structural design.

Truss Bridge Report

Charlotte Simpson

An increased level of stress will occur in areas close to the foundation pads, for this reaso
n we plan to have the
arch and truss structure meet. The foundation base will be strengthened somewhat with interlocking members
joining the truss structure together.

Section 1 of 3

(Same unit used as Section 3)

Section 2

of 3

Combining Sections 1, 2 & 3

Compression Tension Diagram
(Section 1

& 3
)

Structural Analysis

Warren Truss Section

Section
2 is sandwiched between section 1 & 3. To ensure stability in all directions the three
sections are connected to one another using more small diagonal sections of straw.

The truss
pattern alternates as you lo
ok through the lower section of the bridge, aiding stability in all
directions. The photograph to the right illustrates this
.

Truss Bridge Report

Charlotte Simpson

We

looked at the truss structure of our design to carry out our structural analysis. The shaded areas show the
areas we originally ignored when carrying out our calculations, the warren truss is repetitive and symmetrical
so only a few sections are needed to

be calculated before results can be mirrored.

The Analysis

There are two upward reaction forces (RF) and a total of 11 downward forces labelled (Load A). As the bridge is stable the
forces acting in the vertical direction must be in equilibrium, i.e:

Calculating Joint B (JB)

Forces acting upon JB: Load A & C
ompression force of JA

These can be plotted using parallelogram law;

> Resultant vectors directed towards the right indicate pure compression.

> Resultant vectors directed towards the left indicate pure tension.

.
.
. JB
-
BC is acting under compression

JB
-
JD is acting under tension

Calculating Joint C (JC)

Forces acting upon JC: Tension of JB & Tension of JA

JC
-
JE can be found through use of parallelogram law:

The resultant vector is shown directed towards the right .
.
. JC
-
JE is in tension.

JC
-
JD must be in compression to compensate for pulling force of JC
-
JB and JC
-
JA.

Calculating Joint D (JD)

Forces acting upon JD: Compression of JD
-
JB & Compression of JD
-
JC

JD
-
JE can be found through use of the parallelogram law:

The resultant vecto
r is shown directed towards the right .
.
. JD
-
JE is in tension

The counterbalance of this force will be JD
-
JF, .
.
. JD
-
JF is in compression.

The Pattern?

After working out the forces on the fourth joint a
2RF = 11A

RF = 11A/2

.
.
. RF = 5.5A

Calculating Joint

A (JA)

Forces acting upon JA: Load A & RF

Both of these forces act upon the y planar and can
be combined: RF
-
A

5.5
-
1

=4.5A

Plotting forces JA
-
JB, JA
-
JC and 4.5A we find JA
-
JB is
acting under compression and JA
-
JC under tension.

Truss Bridge Report

Charlotte Simpson

pattern became apparent, we predict the following te
nsion & compression diagram for the warren truss section of our
bridge:

(Navy

Compression, Sky Blue

Tension)

Arched Truss

Propos
ed Design:

This bridge was designed from the central vertical member. The table below shows angles used to position members of the
upper and lower chord, and diagonals moving away from and including the centre, from left to right. Values can be used to
m
easure opposite side of bridge as it has a symmetrical design.

Centre

C + 1

C + 2

C + 3

C + 4

Upper Chord

0

-
10

-
24

-
36

-
48

Lower Chord

0

-
6

-
24

-
31

-
36

Diagonal

90

55

51

49

48

Structural Analysis

Compression & Tension Diagram

Arched Section

Arches are naturally strong shapes with the ability to
disperse loads evenly throughout their form. The arch
created will integrate
triangular structures to strengthen
and aid stability. The arch will attach to the warren truss
structure somewhere close to the foundation pad.
Hopefully this will ensure good flow of forces from the top
to the bottom of the structure.

All vertical members and those included within the bottom
deck are under compression. The upper deck and diagonal
members undergo tension.

The arch has been designed with two sharp edges. The
entirety of loads applied to the bridge will transfer through
t
hese points directly into the Warren truss. It’s essential
the bridge is made accurately and is symmetrical to ensure
even load distribution upon the lower structure

Calculating Joint A (JA)

Forces acting upon joint A: Reaction Force &

Both these forces are acting in the vertical plane and can be
combined to give one singular force.

In total there are 13 areas for Load A to act and two areas upon
which reaction forces occur.
.
.

&

RF = 2
.

The bridge is in equilibr
ium so the vertical forces must balance;
the forces acting downwards must equal that of the upwards
forces.

2RF=13A

RF=
6.5A

Vertical Force = 6.5A

A = 6.5A

1

= 5.5A

Truss Bridge Report

Charlotte Simpson

Calculating
Joint A (JA)

(cntd)

We can make use of parallelogram law here as there are only
either pure compression or pure tension acting upon the
members of the truss.

The resultant vector for JA
-
JB points to the right. This means
JA
-
JB is in tension.

The resultan
t vector for JA
-
JC points to the left. This means
JA
-
JC is in compression.

Calculating Joint B (JA)

Forces acting upon joint B: the compression of JA
-
JB

& JB
-
JC.

Again parallelogram law can be used,

here we also make use
of resultant vectors to find ot
her forces.

As the bridge is in equilibrium, once JB
-
JD has been found it
can be assumed JB
-
JC is the opposing force of equal
magnitude.

Calculating Joint C (JC)

Forces acting upon joint C: Load A a
nd tension of JC
-
JA

The resultant force JC
-
JA is directed along the lower right
direction, this force is undergoing tension.

JC
-
JD is directed along towards the upper right quadrant,
this is also undergoing tension.

Calculating Joint D (JD)

Forces
acting upon joint D: Compression of JD
-
JB and JC
-
JD

The resultant force JD
-
JE is directed towards the right, this
member must be under compression. As the bridge is in
equilibrium member JD
-
JF must be under a force of equal
magnitude but in the opposite di
rection, this member will
be under tension.

Calculating Joint E (JE)

Forces acting upon joint E: Tension of JC
-

Using the parallelogram law you see member JE
-
JF is
directed towards the right, indicating tension.

Member JE
-
JD is the result an
d opposite force of JE
-
JF, this is
directed leftwards indicating compression. The magnitude of
both these forces is equal.

Member JE
-
JG is also under tension, the only forces acting
upon this are load A and the compression of JF
-
JG.

Visible Patterns

withi
n Diagram

When looking at the compression tension diagram being slowly created you see all vertical members and those present on
the lower chord are coloured navy, illustrating compression. The upper chord and diagonals are all sky blue, illustrating
tensi
on. The pattern is symmetrical right through the structure, as a group we decided this pattern would continue across
this planar section of the structure.

Truss Bridge Report

Charlotte Simpson

Constructing the Final Truss

With both the arch and warren truss diagrams were firstly drawn accurately on card, pieces of straw then cut
and angled according to the drawing. Once all pieces were cut and placed in accordance to the design it was all
stuck together using a glue gun. In
dividually both sections of bridge were
fairly misshaped,

once joined
together the bridge instantly stiff
ened and became rigid.

To strengthen the arch members were crossed between the two sections. The two sections of arch attached to
section 1 & 3 of
the Warren truss. The photographs below show this.

Predicted Failures

Warren Truss & Arch Joint

Although the structures have been linked together successfully to create one bridge should a great enough load be applied
it’s likely the structure could br
eak here. The bridge as two separate structures has had more time to dry and set, the
weakest joints will be found where the structures meet.

Upper Chord Members of the Arch

The strength of the upper chord depends upon where the load is positioned during
testing. Should it be placed on top of a
joint the arch will be able to withstand a large load
, the forces will transfer directly into the warren truss through the
arches vertical members.

If however the weight is applied between the joints, the load the
bridge is able to carry depends greatly upon the strength
of the straws and not the structural design. The straws are strong when a force is
applied

through them vertically, but
when transferring across them in a fairly horizontal manner they can crush. For this reason we chose to use the thicker and
stronger of the straws for using within the chords on both bridges in an attempt to strengthen these a
reas without stacking
straws.

We could have doubled these straws within this area, we didn’t think this would strengthen this section of the
bridge much and would just add weight to the structure, reducing our load : weight ratio.

Joints

Collectively

Joints include areas where materials meet. Our model could break at these points, dependent upon the rigidity and
strength of the glue used. The joining material has differing physical properties to those of the straw, different forces wil
l
have different
effects upon each and could shatter the structure.

Testing

Model Weight: 125g

Ratio:

Failure: The net was positioned across the
arches members, the bridge itself remained
fine the straws however crushed under the
eight.

Truss Bridge Report

Charlotte Simpson

Summary

The bridge worked well. Throughout this task we worked well as a team and collectively designed and created
a sophisticated bridge with a good weight: load ratio.

The bridge may have had a higher max load had we moved the net when testing on the rig. The amount hung
from our bridge however was above the set 10N, our designed bridge
met the brief.

We could also have increased our weight: load ratio had we substitute
d some straws for stringed sections. This
however can only be done on areas where pure tension’s occurring.

The arch may have held more weight also had it been stiffened slightly. The arch had poor lateral stability
when compared as a separate component t
o the warren truss, had we included more diagonal members to
join the two arch sections our structure may have increased in stability.