ENES102 Truss AnalysisTEAM 1

By Steven Gunter, Sebastian Day, Raul Benavides, William Kaloss, and Akshay Lingayat

Table Of Contents

Table Of Contents

Section 2: Introduction - Ralph Benavides

Section 3: Experimental Material and Property Data and Calculations -Sebastian Day

Section 4: Truss Design-Sebastian Day

Section 5: Support and Internal Reaction Calculations-Steven Gunter

Section 6: Buckling Calculations-Sebastian Day

Section 7:Calculation of Shear Forces,Shear Stresses,and Safety Factors-Steven Gunter, William Kaloss

Section 8: Prediction of Strength-to-Weight Ratio- Akshay Lingayat, ralph Benvides

Section 9: Test Results-Akshay Lingayat

Section 10: Discussion of Test Results-Akshay Lingayat

Section 11: Conclusion and Future Recommendation-Sebastian Day

Section 2: Introduction

The purpose of the Truss Design Project was for students to demonstrate their understanding of mechanics, develop their skill at working in groups, and to provide experience creating a final material product. Briefly, the project demanded that each group of students create a truss which would support 1200 lb. In addition, each group had to maximize the efficiency of their truss by obtaining the highest possible strength-to-weight ratio. There were several constraints that each group had to abide by. The trusses were limited in height to seven inches, and in width to 23 inches. All truss members were required to be greater than 3 inches, and each truss had to have at least 6 members.The cross-sectional area of each truss member was required to be equal or less than .50 square inches. Members had to meet at gusset plate junctions, and could not span past their respective gusset plates. Trusses were required to be held together by gusset plates, made of plywood sheets, glued parallel to each member. No truss member could have gusset plate coverage exceeding 30% of the respective member’s length. Trusses had to be constructed out of either red oak, white pine, or poplar wood. Only two choices of adhesive were permitted, Elmer’s glue and Gorilla glue.

Section 3: Experimental Material and Property Data and Calculations

Prior to construction, each team was required to conduct experimental materials testing. There were two tests. The first tested the tensile strength of the oak, pine, and poplar woods. We tested a piece of red oak.The averaged values obtained are as follows:

Pine: 15421 psiOak: 17513 psiPoplar: 15478 psi

The second test required each team to construct a double gusset-plated member connecting two pieces of wood, in our case red oak. We used Elmer’s glue to adhere these two pieces to the two gusset plates, which overlapped, one above and one below the junction connecting the two members. The averaged values obtained from this test are as follows:

Elmer’s on oak: 1141 psiElmer’s on pine: 941 psiElmer’s on poplar: 1122 psiGorilla on oak: 1345 psi

Gorilla on pine: 1016 psiGorilla on poplar: 1206 psi

We chose white pine and gorilla glue for our respective material and adhesive. We chose white pine because it was readily available. This was our primary motive for choosing this material. Gorilla glue was chosen because it was deemed the strongest from the above values.

It should be noted here that the value for the elastic modulus, E, of white pine, is 1.5 Mpsi, according to Appendix B-1 of our textbook, Mechanics I: Statics, Second Edition Ebook Version, by Dally, Bonenberger, and Fourney. The value for the density of pine wood was obtained from engineeringtoolbox.com, and was found to be 22 lb / ft^3.

Section 4: Truss Design

(Overall Design, Shaded Regions Denote Glued Regions)

Our truss design endeavoured to be as simple as possible to manufacture, while still meeting the requirements of the project. We attempted to maximize every aspect of our truss in length, height, and cross sectional area. The length of our truss was designed to be 22.5 inches long, to accommodate any slop in manufacture. Likewise, the height of our truss was 6.5 inches, designed as such to again allow for a margin of error when constructing the truss. To meet this end we designed a 7 member structure that would bear the assigned load of 1200 lb distributed at two points, B and D. Each member of our truss was covered by gusset plates to the maximum allowable length permitted, 30% of the total member length. There was a total of 10 gusset plates, two on either side of each joint. We designed each gusset plate to cover 15% of each member’s length at both ends. We utilized double gusset plate coverage, so that are shear strength was based on double shear. We used Gorilla glue and White pine for our materials.The following is a list of the dimensions of our truss:

Member Lengths:AB = DE = 8.50 in.AC = CE = 10.94 in.

BC = CD = 4.88 in.

BD = 5.5 in.

Angles

M = 35.18⁰N = 65.35⁰O = 49.30⁰

Glued Member Areas (at each end of the member,on each side)

ABglued = CEglued=(.15) * (8.50 in.) * (11/16 in.) = .8765 in.^2

ACglued = CEglued=(.15) * (10.94 in.) * (11/16 in.) = 1.128 in.^2

BCglued = CEglued=(.15) * (4.88 in.) * (11/16 in.) = .50325 in.^2BDglued = (.15) * (5.5 in.) * (11/16 in.) = .5672 in.^2

Section 5: Support and Internal Reaction Calculations

(Centerline Member Diagram)

Section 6: Buckling Calculations

Buckling Formula: Pcritical=

Where E is the Modulus of Elasticity for Pine Wood: 1.5 Mpsi

Where I is the Moment of Inertia for rectangles: (1/12) * (b*h^3) = (1/12) * (s^4)

Where Lu is the length of the truss member not covered by gusset plates.

Member AB/DE

Member AC/CE

(.01867in^4)]/[(7.658(in))^2]

Member BC/CD

Member BD

(Member Dimensions,Orientation, and Glue Coverage Diagram)

(Gusset Plate Coverage Diagram)

Section 7: Calculation of Shear Forces,Shear Stresses,and Safety Factors

Normal Stresses

All cross sectional areas of members:

Normal Stress Safety Factors (on all loaded members)

Shear Stress Values

AB=DE=AB =

AC=CE=AC

BC=CD=BC

BD=BD

Shear Stress Safety Factors (on all loaded members)

Section 8: Prediction of Strength-to-Weight Ratio

Wooden Rod Weights:

Density of Pine Wood: 22 lb / ft3 = (.0127 lb / in3)

Weight AB/DE = (11/16 in )^2 * (8.50 in) * (.0127 lb / in3) = .0510 lbWeight AC/CE = (11/16 in)^2 * (10.94 in) * (.0127 lb / in3) = .0657 lb

Weight BC/CD = (11/16 in)^2 * (4.88 in) * (.0127 lb / in3) = .0293 lbWeight BD = (11/16 in)^2 * (5.5 in) * (.0127 lb / in3) = .0330 lb

Gusset Plate Weights:

Density of Plywood: .710 lb / ft3 = (4.108*10-4 lb/ in3)

Weight Plate A/E = (1 in * 3 in * .25 in) * (4.108*10-4 lb / in3) = 3.081*10-4 lbWeight Plate B/D = (2 in *2.25 in *.25 in) * (4.108*10-4 lb / in3) = 4.621*10-4 lbWeight Plate C = (3.25 in * 2.50 in* .25 in) * (4.108*10-4 lb / in3) = 8.344*10-4 lb

Total Weight = 2*(.0510 lb) +2*(.0657 lb) +2*(.0293 lb) +.0330 lb + 2*(3.081*10-4 lb) + 2*(4.621*10-4 lb) + (8.344*10-4 lb) = .329 lb

Predicted Strength to Weight Ratio: 850.9 lb / 0.329 lb = 2586.3

Our predicted strength to weight ratio was determined by dividing the load of the member that can sustain the highest shear stress by the weight of the truss and was found to be 2586.3. From our calculations we determined that the member with the highest shear stress value was member BD. We can disregard the idea that normal stress would cause failure because although the stress in member AB is 2187 psi the tensile wood strength of white pine is 15421 psi which means that the member is not particularly close to failure. The maximum shear strength of gorilla glue on pine however is 1016 psi and the shear stress on member BD with the glue is 761.2 psi which is pretty close meaning that member BD is the member to fail first. The load used to calculate this maximum shear stress was -850.9 lb. This value is the maximum load that can be applied to the member before failure. From this we predicted the truss to fail in shear with member BD at the top right gusset plate.

Section 9: Test Results

Actual Strength to Weight Ratio: 1308 lb / ( 11.2 oz * ( 0.0625 lb / 1 oz ) ) = 1868.6

Our truss consisted of seven members and five gusset plates and with the 5.5 inch distributed load test was able to withstand one thousand three hundred and eight pounds with a weight of eleven and one fifth ounces. We believed the truss to fail in shear at the top right gusset plate with member BD and in actuality it did. The truss failed at the top right gusset plate where the glue ripped off from member BD and the plate D. This meant that the shear force of the gusset plate and member BD was the weakest out of all the members of the truss and our theoretical calculations coincided with our experimental results.

We found our actual strength to weight ratio to be 1868.6 which was found by dividing the maximum load placed on the truss (1308 lb) by the weight of the truss (0.70 lb).

The reason why our theoretical strength to weight ratio differed from our actual strength to weight ratio was both the difference in maximum loading the truss was able to withstand as well as the overall weight of the truss. The theoretical maximum load we found was the member with the lowest shear force value which was 850.9 pounds and the weight we determined was the sum of the seven bar members and five gusset plates which added to a total of 0.329 pounds. These numbers were only theoretical and the weight we calculated differed from the calculated weight during the test because the weight of the glue used to attach the gusset plate and members together were not taken into account. The weight of the glue is dense and a substantial amount of it was added to the truss causing the total weight to increase significantly from what we calculated without the inclusion of the weight of glue. Because we did not account for the weight of glue in our predicted strength to weight ratio the actual strength to weight ratio resulted in a smaller value than what was determined by our calculations.

(Test Results:Load-Position Diagram)

Section 10: Discussion of Test Results

Our truss failed at the top right gusset plate with member BD in shear. The shear force exceeded that of the glue and thus resulted in failure. We determined the maximum load that can be applied before failure to be 850.9 pounds which resulted in the highest shear stress of 761.2 psi. Failure is reached when the member of highest shear stress is achieved and is why the member BD failed first. From the test it was determined the actual weight of the truss to be 11.2 ounces which converts to 0.700 pounds. The maximum load our truss was able to withstand before failure was 1308 pounds. Using these two values the weight of 0.700 pounds and 1308 pounds we determined the actual strength to weight ratio to be 1868.6 which was lower than our predicted strength to weight ratio of 2586.3. The reason for the difference as explained earlier was due to the exclusion of the weight of glue in the predicted weight of the truss which would lead to a lower strength to weight ratio value. Our theoretical calculations and predictions matched our experimental data in that member BD was to fail first in shear.

Section 11: Conclusion and Future Recommendation

This project demonstrated many successes, and failures, of our design. The greatest flaw in our design was the presence of zero-force members, which, other than providing stability and a frame around which to produce the truss, did not serve to support the weight placed upon our truss. It served to decrease our strength-to-weight ratio, as well. In general, fabricating the truss proved more difficult than it was to design it, primarily because the members became misaligned while being glued. The design phase also had its challenges. The greatest overall challenge was to decide what parameters were to be constants, and which were to be variables. It was often difficult to decide whether or not an angle or a length should remain constant in the design phase.

The greatest feature of our truss was its simplicity to produce. It utilized only seven members, and each member was made as strong as permissible in shear strength. Additionally, our truss was quite strong, breaking at a load of 1308 lb. This was well past our design goal, and stronger than most other trusses in our section.

In the future, this report advises that a truss under similar loading conditions remove or modify members BD and CB so that they bear force. It is critical that the members connected to joints at either ends of the truss, at the supports, do not directly connect to the points of loading, as our support members did. If this precaution is taken, this report believes that this will prevent the outer, support joint members from bearing all the vertical loading from the loading points.