ANALYSIS OF A 3-D ROOF TRUSS

NAME : Tissera P.M.R.

INDEX NO : 110582T

GROUP : D

DATE OF SUB : 26.02.2014

Specific problem parameters

Civil index number = 107

107 mod 4 = 3

Hence, corresponding data set is data set 4

d 1200L 4800S 1140

The following assumptions were made during modelling and idealizing the structure

1. It is assumed that the joint are pinned, so M3 moment releases were applied2. For purlins, 50x25x8 channel section was used – linear density = 3.86 kg/m

Characteristic loads and material properties

Material properties

Steel – S275o Unit weight = 77 kN/m3

Concrete – G25o Unit weight = 25 kN/m3

Characteristic loads

Live load

Imposed load considering no access type = 0.6 x 4.8

= 2.88 kN/m

Dead load

Roofing sheetso Mass per 1 m2 = 5 kg

Loading = 5 x 9.81 x 10-3 x 4.8

= 0.24 kN/m

90x90x8 L angles and 90x90x8 double angleso Mass of an angle section per 1 m = 10.9 kg

Loading = 10.9 x 9.81 x 10-3 x (4 x 1.2 + 1.408 + 2 x 1.2) / 1.140 = 0.8 kN/m

Channel section for purlins – 50x25x5o Mass of the section per 1 m = 3.86 kg

Loading = (3.86 x 9.81 x 10-3 x 4.8 x 9) / (8 x 1.140) = 0.18 kN/m

Wind load

Take wind load as xxx.xx m/s for the building

Manual calculations for estimating axial force of top and bottom chords

Graphical view of the model in 5 a

Graphical views of the model in step 5.c.

Dead load

Live Load

Validation of the model

Input loading

Output reactions

Comparison of results obtained from different 2-D analyses in 5.a.

Member Internal force

Analysis casePinned-pinned Pinned-roller Fixed-pinned

Top chordAF +33.17 -45.04 33.72SF 4.43 4.43 4.43

BM -0.98 0.99 -0.99

Bottom chordAF -20.04 +43.92 -19.77SF -0.40 0.23 0.197

BM +0.38 0.177 0.157

VerticalAF -26.61/ +11.83 -31.34 -26.65/ +18.95SF n/a n/a n/a

BM n/a n/a n/a

DiagonalAF -31.01/ +21.12 26.67 +21.17/ -32.66SF n/a n/a n/a

BM n/a n/a n/a

Graphical view of the idealized 3-D model

Deflected shape

Axial force diagram

Shear force diagram

Bending moment diagram

Comparisons of design load from 3-D and 2-D analyses

Member Internalload type

Main Truss Secondary2D pin-pin 2D pin-roller 3D 3D

Top chord AL -58.2 -181.451 -177.2 +0.78SF +4.49 +4.506 4.5 -1.59

BM -1.08 -1.08 -1.09 +0.51Bottom Chord AL -78.407 +176.23 +86.08 -0.81

SF +0.24 +0.415 +4.79 +1.96BM +0.24 -0.57 +4.55 +0.68

Vertical AL -36.68 -57.09 -9.97 -0.21SF N/A N/A N/A N/A

BM N/A N/A N/A N/ADiagonal AL +30.52 +56.86 +11.7 +0.18

SF N/A N/A N/A N/ABM N/A N/A N/A N/A

Column AL -60.47SF -28.06

BM -106.34

Discussion

Important factors considered during structural idealization

Analyzing and designing structures to fulfill various requirements are two main problems that a civil engineer has to tackle. To analyze various structure, the civil engineers have various methods that have been developed. Since these methods are developed on different theoretical approaches, the civil engineer needs to make sure that the structure he is going to analyze is compatible with those necessities. But, in many occasions, it does not happen. In other words, real world structures does not made of just simply supported beams and pin joints. Hence, it is the duty of the civil engineer to idealize the real world structure so that it consist of basic structural elements and can be analyzed using the methods in use.

The idealizing of the structure gives the opportunity to see the structural behavior, provided that the idealization is closer to the real world structure. Otherwise, the results we obtain through the real world structure will not represent the actual internal forces of the real world structure.

Hence, according to the specific problem and the type of the solution we are interested in, we can think about the following factors in the process of idealization.

1. Required precision level and the importance of the solution2. Idealized model can be able to solve using the methods in use3. Boundary conditions should be conservative, but compatible with the real structure4. Degree of indeterminacy of the real structure

Anyway, structural idealization is a very important step in analyzing a structure, because it decides the accuracy level of the results we obtain through the computations and the mathematical computations become a minor factor in making the results reliable compared to the importance of structural idealization.

Advantages and disadvantages of using structural symmetry to make the computer model

Advantageso Easier to model in computero Easier to do the manual calculations (for computer analysis, it may be less time

consuming for complex structures, but for simple structures, the difference will not be able to see with modern computers)

o Disadvantages

o It can be difficult to decide boundary conditions for the half of the structure

Reasons for having roller support at one end rather than having pin supports at both ends

In actual structure we consider here is a set of roof trusses that rest on concrete columns. Due to the loads applied, the structure will deflect, causing internal forces. When we consider the real structure, the columns will deflect and that can be more or less idealized with roller support action. Then also, the roof truss will rotate over the columns and this is somewhat similar to the pin supports.

If we look in to the results from the analyses with different boundary conditions, we can see that the 3-D structural analysis gives results somewhat in between these two boundary conditions, and hence it is necessary to experiment with these two conditions and find the best solution.

2-D vs. 3-D modeling

All the real world structures are three dimensional, and also most of the structures we have to analyze are not simple beams or trusses that can be idealized in to 2-D models with little effort. But, if we look in to details, it can be seen that many of the structures in real world can be idealized in to a combination of 2-D structures so that we can tackle the problem easily to obtain a reliable answer. (It should be noted that some architectural designs cannot be idealized in to 2-D models and we have to analyze the structure in 3-D)

The most important things that should be considered in idealizing the 3-D structure in to 2-D models, are the applied loading and the degrees of freedom available. If we can idealize the 3-D structure carefully in to 2-D models, it is very easy to analyze it and we will be get a detailed insight about the structure.

Importance of having secondary trusses in a roof truss

If we consider the one end pinned and the other end on roller situation to be the idealization of our 3-D roof truss in 2-D, from the results we can see that in 3-D truss where there is a secondary truss present, the internal forces are somewhat lower than in the 2-D situation. Hence, the first point that makes the using of a secondary truss important is it reduces the internal forces on the main truss.

And also, the main trusses can be considered to be 2-D structures, and secondary trusses are the structure that combines the 2-D structures in to a 3-D structure.

Welded connections vs. bolted connections

Both of these methods are in use and depending on the context, both the methods have their plusses and minuses.

If we consider welded connections, it needs skilled labor and it is not cheap. Then, the special equipment are needed for the procedure. Also, the parts will not be disassembled. But, on the other hand, welding is less time consuming than bolting and the possibility of corrosion development is much less.

Bolted connections need a hole and this reduces the capacities of the structural member. And also, this drilling process consumes a lot of time. The bolting alone does not need special skills as in welding, and also the spanner and a pair of pliers will be sufficient for most of the occasions. Then, the assembled parts can be disassembled at another time for a different requirement.