Final Report CEE 4803 Balsa Wood Bridge Design Project 

December 9, 2015   

Group 3 Arman Yosal Josia Tannos Maya Goldman Savannah Brooks 

                  

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                    

           

 

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                             

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. 

  

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. 

 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 

 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 

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. 

 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 

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. 

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 

  

 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.       

   

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" 

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 

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 

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) 

Deflection (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)