This document summarizes a student group's balsa wood bridge design project. It describes the concept, design methods, construction techniques, testing and performance, and post-test evaluation of their simple warren truss bridge. The bridge was designed to support a 15 pound load but was tested to failure at over 20 pounds. It was constructed of balsa wood pieces laminated with glue and gusset plates. Testing showed it exceeded the design requirements and failed due to cracking of cross bracing members in the center of the span.

1. Final Report
CEE 4803 Balsa Wood Bridge Design Project
December 9, 2015
Group 3
Arman Yosal Josia Tannos
Maya Goldman Savannah Brooks

2. Table of Contents
I. Introduction……………………………………………………………………….....page 1
II. Concept…………………………………………………………………………....page 2­3
III. Design Methods……………………………………………………………………..page 2
IV. Construction Techniques………………………………………………………….page 3­7
V. Testing and Performance………………………………………………………….page 7­8
VI. Post Test Evaluation……………………………………………………………..page 8­10
VII. Conclusion………………………………………………………………………....page 10
VIII. Appendix

3. I. Introduction
This report covers the initial ideation and design, construction, testing and failure analysis
of a balsa wood truss bridge with span of forty inches, height of six inches and width of four
inches and a weight of 135.9 grams. Using SAP2000 the three dimensional simple warren truss
model was loaded with a thirty pound distributed force to account for a factor of safety of two.
The bridge was constructed by laminating together wood pieces using super glue, included
gusset plates to act as joints, and consisted of a platform to take into consideration how the
bridge would be loaded during testing. The performance of the bridge exceeded expectations by
holding twenty­eight percent more weight than it was designed for and failed spectacularly by
multiple lateral cross bracings and frame members splintering or cracking at the center of the
span. The following sections will describe in more detail the design methods, construction
techniques, testing and performance, and post test evaluation.
II. Concept
Before construction could commence, a suitable design had to be chosen. The primary
goal for the preliminary plans was to create the most efficient system possible. This means that
the bridge should be efficient in terms of cost by being conservative with material orders. It was
also designed to be efficient in terms of loading capabilities. This means that the bridge was
designed to withstand the 15 pounds of applied load required but not much more after that. It The
goal was to create a bridge that would fail as close to this weight requirement as possible while
still meeting the 0.25” maximum deflection allowance using the least amount of material
necessary. In order to do this, various typical truss designs were examined. In the end, a simple
warren truss design was chosen based on its overall symmetry and redundancy which would
allow for uniform self weight distribution and ease of construction. After this, hand calculations
were completed in order to ensure forces on each member fell below the minimum weight
requirement. The minimum requirement was 15 pounds, however, in order to prevent the
possible hindrances and performance issues during testing caused by possible human errors made
during the construction process, a safety factor of two was applied to the system. This means that
calculations for forces on each member were calculated using a load of 30 pounds, instead of 15
pounds. This was to give more leeway during performance testing. These calculations were
completed for simple warren trusses that contained varying amounts of triangles. These designs
were then eliminated until two possible choices remained based on the height and span
constraints given as project requirements. The options for the truss was either a five triangle truss
or a seven triangle truss. Ultimately, the design with seven triangles was chosen as can be seen in
Figure 1a. Finally, the design was put into SAP2000 in order to create a model as close to real
world system loading behaviors as possible. The 3D model created in this program was
constructed for the idealized case of loading on the center lateral member. A factor of safety of
two was also applied to this model. Modeling the design in SAP2000 gave more exact estimates
of how the structure would react when the load is applied, allowing possible points of

4. weaknesses to be documented and strengthened during construction, lessening the chances of
premature system failure.
III. Design Methods
An integral component of the design process after the initial design concept had been
completed was planning the cross sectional area of each member in the truss. This was calculated
using a form of the stress equation, and balsa wood properties found in Table 4a.The P,A = σ
maximum stress each member can hold is 0.68 ksi for compressive stress and 1.10 ksi for tensile
stress. The results are shown in Table 2a. Four different cross­sectional areas were used in order
to build the truss bridge. All of these can be seen in Table 5a. The materials ordered then can
seen in Table 1a. Without considering cross­sectional area, the deflection exceeds the criteria.
Deflection decreases with increased cross­sectional area. So, in the final model, the
cross­sectional area of some members were increased to reduce the deflection. For example,
member HJ in the center of the truss was designed to have a cross sectional area of ⅜” by ⅜”.
This was achieved by laminating four 3/16” pieces together.
Deflection tests were also completed once all materials ordered had arrived. This was
done in order to calculate the properties for each piece since balsa wood properties can vary from
piece to piece. After completing the test, it was determined that the calculated modulus of
elasticity was ten times greater than that the accepted one published online. These properties
found through testing were not used, however. Altering these properties in SAP2000 would have
altered the entire design and the materials required. As engineers, efficiency in terms of cost and
time are of the utmost importance, both of which would have been sacrificed should these new
values been used. These properties could have been used, if samples of the material were
provided in order to complete deflection tests before material orders go out or if it were possible
to reorder materials.
Another component of the truss design is lateral bracing along the top and bottom, in the
shape of X’s. These lateral bracing members were placed to join each section of the frame except
the center where the load was applied. These elements were added to account for torsion due to
human error during the construction of the structure. However, since these were added merely to
add stability should the bridge be slightly misshapen or skewed and since the cross sectional area
of these pieces is moot, the smallest available cross­sectioned pieces were used. This was done in
order to limit the amount of weight added to the structure. Thus, the 1/16” pieces of Balsa wood
were used. Another design detail to account for loading is the top center member where the load
bar was placed. In order to create a strong platform to rest this bar on, three pieces of 3/16” balsa
wood were placed on top of the center member to create a platform just over half an inch wide.
Also, gusset plates were used at each of the joints in order to increase stability at these possible
points of weakness.

5. IV. Construction Techniques
First the materials were gathered and counted to ensure all necessary items were
purchased and collected. See Table 1a. of the appendix for material order. T­squares (metal
rulers shaped like a T) and X­Acto knives were used to cut all the member pieces to the correct
lengths based on the dimensions of the bridge design seen in Figure 1. The amount of each piece
with specified length and cross­sectional area were tabulated in Table 3a. and used during this
cutting process to keep track of how many of each kind were needed. In order to keep the cuts
consistent, the members were made slightly longer so that the length was a mark on the ruler as
opposed to in between two marks.
a. Front view of truss
(b) Side view of truss
Figure 1. Dimensions of truss members based on design concept and methods and minimum
requirements of 36” length by 4” width by 5” height
After all the pieces were cut, they were laminated together to make the necessary
configuration. For example, to make member AB ¼” X ¼”, four ⅛” pieces of length 5.7” were
glued together. This was done for every member twice to create the two frames and these were
taped together and labeled for easy access when connecting all the pieces together at a later time.
Next the gusset plates were cut to 1.5”X1” except at the connection joints F,H, and J where the
dimensions were cut to 1.5”X1.5” to account for the larger members. Two gusset plates on either
side of the connection and for two frames resulted in cutting sixty total. Finally, small pieces
were cut and glued to the ends of each member which was connected to a member thicker than
itself, so that at the connection all members were touching the gusset plates.

6.
Image 1. Laminated piece on small member (red circle) to increase height (green line) and create
connection to gusset plate
Before construction all the pieces were laid out in their proper positions and there was a
discussion about how to form the connections so that the proper angle for each triangle was
maintained. A hand­drawn sketch was used as a template, and the pieces were placed on the
template. The first corner, A, was the starting point. Each connection was formed by glueing the
members to the gusset plate so the triangle matched the template, and the frame was moved each
time to form the next triangle. This method, however, was flawed since the template did not take
into account the thickness of the members or the actual connection size, nor were the lines
perfectly straight. It was also difficult to gauge the linearity of the overall structure as it grew
because each triangle was formed relative to the template instead of the overall frame. To combat
most of these issues, a CAD drawing was printed on a plotter to actual size, which replaced the
hand­drawn template.
Image 2. Laminated members organized in shape of truss

7.
Image 3. Hand drawn template method Image 4. CAD template method
While the first truss frame was being finished, the next frame was created by aligning the pieces
on top of the existing frame and then glueing the members to the gusset plate, starting at the
corner and working left to right towards the other corner. This method was chosen for schedule
efficiency and because after the first frame was complete it was more important for the two sides
to be exact copies of each other than for the new frame to follow the template (symmetry).
Image 5. Second truss built on top of first truss

8. Next, the two frames had to be connected with lateral bracing and cross­bracing. In order
for the two frames to remain vertical and at the correct distance apart when glueing the lateral
bracing members to either side, tongue depressors hole punched at either end and clamped
together with a screw and nuts were secured along the length of the bridge as seen in Image 6.
Image 6. Tongue depressor system used to stabilize truss frames when adding lateral bracing
Once group members confirmed the width between frames at both ends of bridge were equal and
the frames were perpendicular to the table (not leaning or rotating), a lateral member was glued
on either end and placed between the frames, with a gusset plate at the top of the ⅛” members.
The 3/16” members were simply glued to the frame without gusset plates.
Image 7. Gusset plates on ⅛” lateral members Image 8. Connection for 3/16” members
The cross­bracing pieces of size 1/16” were cut and glued on an individual basis after the whole
bridge was built. These pieces were glued to the truss frame without gusset plates.

9.
Image 9. Cross­bracing top view
V. Testing and Performance
First, the supports of the bridge at each end were placed on the table. The supports in contact
with the table must not exceed 0.5 inches according to project specifications. One shim was used
on the right back support (based on Image 10 configuration). The bridge was tested by placing a
steel metal bar on the platform at the top center of the bridge. Then, a chain was used to lift the
bucket filled with loads. The loading started with ten pounds and weight was added until the
bridge failed. The configuration of the bridge and the loading is shown in Image 10.
Image 10. Loading the bridge

10. The bridge was expected to have a minimum height of five inches, minimum width of four
inches and minimum length of 36 inches. As shown in Table 1, the bridge met the height, width
and length requirements. Another specification was that the bridge was expected to deflect no
more than 0.25 inches. When a load of 15 pounds was applied at the center of the bridge, the
deflection was almost zero.
Table 1. Measured values during testing
Height 6 in
Width 4 in
Length 40 in
Weight of bridge 135.6 g
Weight of load at failure 53.5 lb
VI. Post Test Evaluation
Image 11 shows the failed segment of the bridge. The bridge failed at a load of 53.5 lb. It
can be seen that the bridge underwent shear failure at the gusset plate. Image 12 and Image 13
show the shear failure observed on the bridge. There were no members that broke because of
axial forces. This shows that the member cross­sectional area is large enough to withstand the
axial stress caused by the load. The lateral members mostly remained intact across the span. This
shows that the lateral members used were strong enough to withstand the torsional load due to
the unsymmetrical shape and load offset. It is shown that the wood splintered at the connection at
point H and I. The member was not able to withstand the shear force caused by the load.
The goal of this project was to design a bridge that can withstand 15 lb load located at the
midspan of the bridge. This design was created by accounting for a factor of safety of two. The
cross­sectional area of the members were calculated so that the deflection is not more than 0.25”.
Based on the test result, the ultimate strength and elastic modulus used in the SAP analysis were
lower than the actual value. In the design, the amount of material was added to meet the
deflection requirement. At first, by using smaller cross­sectional area for each member, the
designed was able to hold up to 30 lbs. However, the initial design showed that the deflection
was 0.70 inches, which is more than the maximum deflection. In order to reduce the deflection,
the members must have larger cross­sectional area because the deflection of truss is inversely
proportional to the cross­sectional area of the members. During the test, the bridge does not
deflect significantly (the deflection is close to zero) and it can be concluded that the bridge was
over designed. This over design was due to lack of understanding of the balsa wood properties.
The balsa wood used in this project were stiffer than the assumed elastic modulus and therefore a
more efficient design could have been used. Moreover, by increasing the cross­sectional area of
each member in the truss, the weight of the structure also increased.

11. The span and height of this bridge exceeds the minimum requirement specified. This
truss bridge spanned 40 inches while the requirement only specified a span of 36 inches. This
truss bridge had a height of 6 inches while the requirement only specified a height of 5 inches.
This extra span and height induced more weight in the bridge. This happened because the design
plan did not account for extra length in the connection and the thickness of the member. This
additional length and weight increase the weight of the bridge.
Image 11. Failed Segment of the Bridge
Image 12. Failed Gusset Plate

12.
Image 13. Shear Failure at the Horizontal Component.
VII. Conclusion
This design was able to withstand fifteen pounds of load located at the midspan of the
bridge. In the design process, a factor of safety of two was used to account for human errors,
defects in materials and other factors that may affect the performance of the bridge. After the
test, the bridge was able to carry 53.5 lb before failure. Moreover, when a load of fifteen pounds
was applied, the bridge did not deflect significantly (the deflection was almost zero). These
indicate that the bridge was over designed because it could withstand more than the expected
load and the actual deflection was smaller than the expected deflection. This is caused by
underestimation of elastic modulus of the balsa wood. The expected length and height of the
bridge was thirty­six inches and five inches respectively. However, the actual length was forty
inches and the actual height was six inches respectively. This is caused by the thickness of the
material and the space between members at the connections that were not considered in the
design process. This additional length and height increased the weight of the bridge. Overall, this
design could be improved by using a more accurate elastic modulus and accounting for
additional length and height at the connection as well as the thickness of the members.

13. VIII. Appendix
Table 1a. Material order for balsa wood
Size Amount
1/16” 5
⅛” 31
3/16” 4
Plate 1
Table 2a. The force in each member with factor of safety of two based on SAP2000 analysis
Members Force (lb)
Direction of
Force
Minimum Cross­Sectional Area
(in 2
)
Configuration of
Member
AB ­8.46 Compression 1.24E­02 1/4" x 1/4"
AC 3.9 Tension 3.54E­03 1/4" x 1/4"
BC 8.46 Tension 7.66E­03 1/8" x 1/8"
BD ­7.8 Compression 1.14E­02 1/4" x 1/4"
CD ­8.46 Compression 1.24E­02 1/4" x 1/4"
CE 11.72 Tension 1.06E­02 1/4" x 1/4"
DE 8.46 Tension 7.66E­03 1/8" x 1/8"
DF ­15.62 Compression 2.29E­02 1/4" x 1/4"
EF ­8.46 Compression 1.24E­02 1/4" x 1/4"
EG 19.52 Tension 1.77E­02 1/4" x 1/4"
FG 8.46 Tension 7.66E­03 1/4" x 1/8"
FH ­23.42 Compression 3.43E­02 3/8" x 3/8"
GH ­8.46 Compression 1.24E­02 1/4" x 1/4"
GI 27.32 Tension 2.48E­02 1/4" x 1/4"
HI ­8.46 Compression 1.24E­02 1/4" x 1/4"

14. HJ ­23.42 Compression 3.43E­02 3/8" x 3/8"
IJ 8.46 Tension 7.66E­03 1/4" x 1/8"
IK 19.52 Tension 1.77E­02 1/4" x 1/4"
JK ­8.46 Compression 1.24E­02 1/4" x 1/4"
JL ­15.62 Compression 2.29E­02 1/4" x 1/4"
KL 8.46 Tension 7.66E­03 1/8" x 1/8"
KM 11.72 Tension 1.06E­02 1/4" x 1/4"
LM ­8.46 Compression 1.24E­02 1/4" x 1/4"
LN ­7.8 Compression 1.14E­02 1/4" x 1/4"
MN 8.46 Tension 7.66E­03 1/8" x 1/8"
MO 3.9 Tension 3.54E­03 1/4" x 1/4"
NO ­8.46 Compression 1.24E­02 1/4" x 1/4"
Table 3a. Length, cross­sectional width, and number of pieces to be laminated for each member
Member Label Wood Cross­Section
Size (in)
Length (in) Amount
AB 1/8 5.7 4
AC 1/8 5.2 4
BC 1/8 5.7 1
BD 1/8 5.2 4
CD 1/8 5.7 4
CE 1/8 5.2 4
DE 1/8 5.7 1
DF 1/8 5.2 4
EF 1/8 5.7 4
EG 1/8 5.2 4

15. FG 1/8 5.7 2
FH 3/16 5.2 4
GH 1/8 5.7 4
GI 1/8 5.2 4
HI 1/8 5.7 4
HJ 3/16 5.2 4
IJ 1/8 5.7 2
IK 1/8 5.2 4
JK 1/8 5.7 4
JL 1/8 5.2 4
KL 1/8 5.7 1
KM 1/8 5.2 4
LM 1/8 5.7 4
LN 1/8 5.2 4
MN 1/8 5.7 1
MO 1/8 5.2 4
NO 1/8 5.7 4
AA' 1/8 4.2 1
BB' 1/8 4.2 1
CC' 1/8 4.2 1
DD' 1/8 4.2 1
EE' 1/8 4.2 1
FF' 3/16 4.2 1
GG' 3/16 4.2 1
HH' 3/16 4.2 3

16. II' 3/16 4.2 1
JJ' 3/16 4.2 1
KK' 1/8 4.2 1
LL' 1/8 4.2 1
MM' 1/8 4.2 1
NN' 1/8 4.2 1
OO' 1/8 4.2 1
*Table 5a. simplifies this data to show totals for each cross sectional size
Table 4a. Balsa wood properties based on flexural test
Trial Length
(cm)
Width
(cm)
Moment of
Inertia
(cm^4)
Load
(N)
Length
(cm)
Deflecti
on (cm)
Elastic
Modulus
(GPa)
1 0.318 0.318 0.001 0.196 25.000 1.800 6.704
2 0.318 0.318 0.001 0.196 25.000 2.200 5.485
3 0.159 0.159 0.000 0.098 10.000 1.000 6.178
4 0.159 0.159 0.000 0.098 10.000 1.500 4.119
Table 5a. Cross sectional area of Members
Cross Sectional Size Number of Members Pieces Laminated
1/4" x 1/4" 38 4 x (1/8" balsa wood)
1/8" x 1/8" 8 4 x (1/16" balsa wood)
3/8" x 3/8" 4 4 x (3/16" balsa wood)
1/4" x 1/8" 4 2 x (1/8" balsa wood)