AKDEṄ IZ ÜVVERṠ ITEṠ I
̇ I NS ̧AAT MÜHENḊ ISLK FAKÜLTEṠ I BLMSEL ARATIRMA TEKNKLER ̇ I VE EṪ IK-I DERS YÜKSEK L̇ ISANS
Student: Mohammad Eiraj Shakib 20165115026
Winter 2017
I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work.
Name, Surname: Mohammad Eiraj Shakib Signature:
I
I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work.
Name, Surname: Mohammad Eiraj Shakib Signature:
I
Table of Contents ABSTRACT ................................................ .......................................................................... .................................................... ......................................... ............... III ACKNOWLEDGEMENT .................................................. ........................................................................... .............................................. .....................IV LIST OF FIGURES.................... FIGURES.............................................. .................................................... .................................................... .................................. ........ V LIST OF TABLES ..................................................................... .............................................................................................. ...................................... ............. V CHAPTER ONE .................................................. ............................................................................ .................................................... .................................. ........ 1 1.1 Introduction ........................................................................................................................................ 1 1 .2 structural analysis and design software ............................................................................................. 2
CHAPTER TWO............................ TWO...................................................... .................................................... .................................................... .............................. .... 2 2.1
Truss systems .................. ................. ................. .................. ................. .................. .................. ..... 2
2.1.1 Planar trusses ............................................................................................................................... 2 2.1.2 Three-dimensional trusses ........................................................................................................... 5
CHAPTER THREE .................................................. ............................................................................ .................................................... .............................. .... 9 3.1 building material ................................................................................................................................. 9 3.2 Disadvantage of steel .......................................................................................................................... 9
CHAPTER FOUR ...................... ................................................ .................................................... .................................................... .................................. ........ 9 4.1 Modeling of Triangular arch truss ....................................................................................................... 9
CHAPTER FIVE ............................................................... ........................................................................................ ............................................. .................... 15 5.1 Analysis of Triangular arch truss ....................................................................................................... 15
CHAPTER SIX ................................................ .......................................................................... .................................................... .................................... .......... 19 6.1 Design of Triangular arch truss ......................................................................................................... 19
CHAPTER SEVEN .................................................. ............................................................................ .................................................... ............................ .. 21 7.1 Summary ........................................................................................................................................... 21 7.2 Conclusion ......................................................................................................................................... 25
References ................................................. ........................................................................... .................................................... ........................................ .............. 25
II
ABSTRACT A truss is a structure comprising one or two triangular units constructed with straight members, whose ends are connected at joints (nodes). External forces and reactions to those forces are considered to act only at the nodes and result in axial forces in the members that are either purely tensile or compressive. Trusses are capable of spanning much further than solid beams or girder members, with less material. Trusses can be planar, box or space type. Thus, there is no limit to the forms that can be created using trusses. In instances of curved geometry, the trusses can be fabricated to incorporate the curved structure into their span. These trusses can use curved members for the top and bottom chords, and straight segments for the web members. Triangular arch trusses are one of these kind which are mainly used in the structure of bridges and roofs. In addition to the manner of acting as a truss, triangular arch trusses use arch action to reduce the bending moments in long-span structures. Essentially, an arch acts as an inverted cable, so it receives its load mainly in compression although, because of its rigidity, it must also resist some bending and shear depending upon how it is loaded and shaped. Triangular arch trusses are almost designed as bending free structures to eliminate any excessive deflection. This graduation project is intended to model, analyze and design triangular arch trusses for an industrial building using SAP2000 computer program subroutines. The thesis starts with a brief information about SAP2000, truss systems and usage of steel as building material for trusses. Then, it shows the process of modeling, analyzing and designing of a canopy step by step. The thesis ends with a model of the skillful structure with reasonable design results.
III
ACKNOWLEDGEMENT Foremost, I would like to express my sincere gratitude to my advisor Assist. Prof. Dr. Nildem Tayşi for the continuous support of my graduation project, for her patience, motivation, and broad knowledge. Her teachings, particularly in structural analysis, helped me in all the time of doing the project and writing of this thesis. My earnest thanks also goes to Prof.Dr.Pallab Das, Prof.Dr. Aminul Islam Laskar, Prof.Dr. A.K. Dey, Prof.Dr.Parthasarathi Choudry, Asst.Prof.Dr .Parbin Sultana, Assoc.Prof.Dr. Nirmali Borthakor, Assoc.Prof.Dr. A.K. Borbhuiya, Assoc.Prof.Dr.Briti Sundar Sil, Dr.Susmita Gosh, Assoc.Prof.Dr.Bijan Kumar Roy, Research Asst. Upendra Kumar and all other precious lecturers who have helped me grasp the fundamentals of engineering so I am able to work on this graduation project at present.
I thank my fellow classmates in University of NIT Silchar : Zarif Noori , Krishneel Sanjay Ram, Abdul Basir Rahmati , Aryan Farahi, Anurag Anand, Nilutpul Chutiya and all the rest for all the fun we have had in the last four years. I am grateful to Abdulrziq hakimi, a graduate student of Civil Engineering, for enlightening me the first glance of the project.
I appreciate all efforts of my family members specially my brothers, Mohammad Ali Shakib , and Eliyas Shakib who always have backed me up. Last but not the least, I would like to thank my parentsTahera Popal and Saifulrahman khan, for giving birth to me at the first place and supporting me spiritually, academically and financially throughout my life. Their existence means the world for me as without them my creation would not be even a night’s dream .
IV
LIST OF FIGURES Figure 1 Types of Planar truss ....................................................................................................................... 3 Figure 2 Purlins ............................................................................................................................................. 3
LIST OF TABLES Table 1: The dimensions of parts of the frame in preliminary design ........................................................ 13
V
CHAPTER ONE 1.1 Introduction This graduation thesis focuses mainly on using Sap2000 as a structural analysis and design software to model, analyze and design an industrial building framed with triangular arch truss supported by steel pipe columns with metal roofing supported by purlins. The main parts and members of the building are triangular arch trusses, columns, girders, purlins, metal roofing and joints. The arch truss used in the building is a triangular space frame truss which its bottom and top chords are made of steel pipe. Each purlin and column has section made of steel tube but of course with different dimensions. The girders connecting the columns are also steel tube. The building frame consists of seven bents*, or in other words it has totally six bays. This is going to be built on a 20m x 36m area .So each bay measures 6m and the span of the arch truss is 36m.The height of each column is 5 m and the radius of the outer arch is 4m. AISC 360-10 * design code is used for the design requirements of this steel structural building.
The second part of this chapter will discuss about Sap2000, its purposes and usages. Chapter 2 will give really good information about truss systems, why and how it is preferred to be used in the structure of the building. In chapter 3, we will discuss about steel as a building material in this project. Subsequently, by using Sap2000 we will show how to model, analyze and design the building in chapter 4, 5 and 5 respectively. Finally, the thesis will be summarized and concluded in Chapter7.
*The roof truss along with its supporting columns is termed as a bent. * AISC: American Institute of Steel construction
1
1 .2 structural analysis and design software SAP2000 is integrated software for structural analysis and design. It is a Finite Element Analysis program created by CSI Inc. SAP uses the stiffness matrix for its analysis. It is used primarily by structural engineers for analysis to determine forces, moments, and displacements. It is especially useful for dynamic analysis of seismically induced motions. From its 3D object based graphical modeling environment to the wide variety of analysis and design options completely integrated across one powerful user interface, SAP2000 has proven to be the most integrated, productive and practical general purpose structural program on the market today. In SAP2000 ,you can develop a computational building model with different kinds of materials, cross sectional dimensions of columns, beams, trusses, etc., and then place different loads on the building model that are needed; after making calculations that go along with codes, specifications and guidelines that a local building jurisdiction would use. Next step is to test the model to ensure its survival. SAP2000 is able to give you a more accurate and precise solution with details than solving the problem by hand.
CHAPTER TWO 2.1 Truss systems A truss is a structure comprising one or more triangular units constructed with straight members, whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and result in axial forces in the members that are either purely tensile or compressive. Moments (torques) are explicitly excluded because all the joints in a truss are treated as hinges or theoretical pin connections. Trusses are capable of spanning much further than solid beams or girder members, with less material. Trusses can be planar, box or space type. A planar truss is two-dimensional, with all of the members lying in essentially a single plane, the loads of the truss being picked up from their end connections. Box-type trusses also span only in one direction but have a three-dimensionality to them that is usually rectangular or triangular. Space trusses are also called space frames. These systems can span in multiple directions, with their loads transferred from any node in the system.
2.1.1 Planar trusses
2
Although there are countless variations of planar truss types, these diagrams outline some of the most common ones.. Fabricated from common steel angles and plates, they represent the least expensive options for fabrication. The top and bottom members of the trusses are referred to as "chords" and the intermediate steel as " web members". Under typical loading the top chord will act in compression and the bottom chord in tension.
Figure 1 Types of Planar truss
Beams and joists are intended to accept loads continually along their length ("distributed loads"). As a result, these members are designed to resist flexural or bending stresses. Trusses are designed as pin- or hinge-connected structures, with the intention to transfer loads axially along each member. Hence the members are designed to resist either pure compression or pure tension, but not bending. Therefore, loads must only be transferred to the truss at its node, panel points or joints.
The steel decking for this roof sits on purlins. Purlins are used to span between trusses and transfer the loads to the truss at its panel points. If the geometry of the connection is precise, the load should be transferred through the centroid of the connection, resulting in only compressive or tensile axial loading in the chord and web members. The further apart the trusses are spaced, the more substantial the purlins will need to be. The dimensioning of the truss itself will be a 3 Figure 2 Purlins
function of the spanning capabilities of the decking, as the spacing of the purlins will be directly impacted. From an architectural perspective, trusses present an enormous design potential for a building. Where common steel trusses are fabricated from standard sections, the fact that there is only pure tensile or compressive axial loading implies that the member selection can be finetuned so as to reflect the nature of the loading. Rods or cables can be used for tensile members, creating a contrast with the use of sections for compression members. This presents unique opportunities for designing the connections between the members in a way to develop an individual architectural detailing language for the project.
The importance of the geometry of the node can be seen in the alignment of the incoming members of this node. An attempt is made to ensure that the centers of gravity of all members coincide at one point.
The long-span Warren trusses at the Canadian War Museum in Ottawa, Canada are fabricated from square HSS members. The web members are slightly smaller in section than the top and bottom chords, making it simpler to fabricate the welded joints. Wide-flange sections carry the load of the steel decking to the trusses. Cross bracing is introduced in the plane of the roof.
4
2.1.2 Three-dimensional trusses Three-dimensional truss systems are used as a means to limit the span requirements of the structural members that carry the roof or floor loads to the trusses. The added third dimension of the truss also provides additional lateral stability in situations of long span. Box-type trusses have a linear span direction. This is very different from a space frame, which can span freely in multiple directions. As with other truss types, loads must be transferred at the nodes to ensure that there is only axial loading of the members. Three-dimensional trusses are typically custom-fabricated for each project. They are often used in architecturally exposed conditions, so member selection and connection design are important. As their connections are often geometrically challenging, round HSS sections are normally used, as it has been found to be simpler to resolve welded connections for this member type.
2.2 Triangular arch truss There is no limit to the forms that can be created using trusses. In instances of curved geometry, the trusses can be fabricated to incorporate the curved structure into their span. These trusses can use curved members for the top and bottom chords, and straight segments for the web members. The metro station in Dubai, UAE and the Amphitheatre called The Bank of America Pavilion in Boston, MA, USA are two famous structures which triangular arch trusses are used as part of their construction.
5
The curved triangular trusses that span across the Dubai Metro stations have single round HSS top chords and a pair of round HSS bottom chords that are separated by smaller round HSS web members. The welded joints combined with the curved steel help to keep the truss stiff in spite of a lack of diagonal web members in the plane of the arch/truss.
6
The fabric roof of The Bank of America Pavilion in Boston, MA, USA by A-Form Architecture, is supported by a single three-dimensional trussed arch. The truss can make use of ground access to assist erection, so it was possible to fabricate the truss as a series of smaller elements.
As it was not possible to fabricate and transport the truss in one piece. It was divided into sections. Highstrength moment-resisting connections were then used to create continuity in the chords. Joints were fabricated by welding plates to the ends of the round ASS members. The connection between the tube and the plate is stiffened by the addition of triangular plates between each bolt hole.
7
Trusses are one of the more versatile framing systems in that they can be used both as spanning members and as inhabitable spaces. If the depth of the truss is sufficient, it is possible to plan around the web members to create usable space. If the basics of connection design strategies and the intentions of framing are well understood, then it is possible to build upon simple solutions to create an innovative architectural language of connections in steel.
2.2.1 The advantages of Triangular arch trusses Triangular arch trusses have many advantages compared to other types of roof structures like two-dimensional trusses, reinforced or pre-stressed concrete beams. Most important difference in triangular arch trusses is three-dimensional load distribution in all parts of the structure. This causes a reduction in the weight of the structure by carrying loads with more members instead of single one, and thus maximum deflection along the structure is reduced. In addition, a separate design of every member in triangular arch trusses increases the efficiency in capacity use of members. Another important property of it is that they are indeterminate systems. This means, the failure of one or a few number of members on the structure does not necessarily lead to collapse of structure completely (Chilton, 2000). By using higher safety margins in some critical members, the resistance of structure against to progressive collapse can be increased. Moreover, triangular arch trusses have large volume of free space between top and bottom chords. This permits to install any type of mechanical or electrical service systems continuously along the structure (See Figure). Additionally, every component of triangular arch trusses is prefabricated, and so the quality of the each part is higher and the tolerance is lower compared to in-situ structures. The modular form also meets variety of architectural requirements easily.
Figure: The free space in trusses permits to install any type of mechanical or electrical service systems
8
CHAPTER THREE
3.1 building material Steel is the material used in the frame of this industrial building. It is light and economic for this type of structures. It is also easy to provide required accuracy in metals. Aluminum is another metal, which can give the same accuracy and it is lighter compared to steel. However, its modulus of elasticity is around 1/3 of the one that steel has. Therefore, maximum deflection in the structure may govern the design. To prevent excessive deflections, higher sections may be required and this may eliminate the lightness advantage of aluminum. Since steel is cheaper compared to aluminum, using steel in the structures is generally preferred all around the world. As a result considering all advantages of steel, we have decided to use steel in this building.
3.2 Disadvantage of steel On the other side, triangular arch trusses made of steel have many disadvantages like vulnerability against fire and corrosion. Without taking any measures, the resistance of tubular structure to fire is negligible. Although there are some solutions like fire protective paints, none of them is economical due to large surface area of members. Corrosion is easier to deal with compared to fire. There are many economical solutions against corrosion in the market. Painting and galvanization are some of them. The rate of corrosion is also very low and foreseeable. However, fire is very sudden and can result in vital hazards.
CHAPTER FOUR 4.1 Modeling of Triangular arch truss As it was mentioned in the introduction, the building frame consists of seven bents, or in other words it has totally six bays. This is going to be built on a 20m x 36m area .So each bay measures 6m and the span of the arch truss is 36m.The height of each column is 5 m and the radius of the inner and outer arch are 18.2m and 19.4m respectively. The main part of modelling the frame is to sketch out the arch. Since it is very much easier to draw it in AutoCAD, we will first draw a 2D arch in AutoCAD and then we will import it into Sap2000 in order to form it into a 3D arch truss by using Duplicate command. So the modelling can be done partially in AutoCAD. The modelling is explained in the following steps: 9
Step 1:
The span of the arch truss is 20.0m.The bottom arch cord’s radius is 18.2m while that of the top is 19.4m. The bottom chord is divided into 20 equal parts. Knowing the dimensions of the truss, it is so easy to draw it in AutoCAD. The parts of the truss should be drawn in different layers in order to be able to define the parts while importing it into Sap2000.
Figure: The chords are drawn in green and web members are in blue. The brown construction lines are drawn to show the symmetry of the arch truss.
Make sure that the origin of the coordinate system of the drawing in AutoCAD coincides with that of Sap2000.So it will be imported exactly within the boundaries of the grid system. After completing the drawing, it should be saved in dxf file format to be imported into Sap2000. Step2: Before importing the file, we should define our grid lines. Grid lines are good for not making any mistakes regarding to the dimensions and location of the members.
10
Figure: The ordinates of the grid lines can be edited by right clicking on the active windows and selecting “Edit Grid Data “
Step #3: After defining the grid data, the file can be imported into sap2000 by selecting the “import “command from the “file” menu. While importing the file, make sure the units are in KN,mm,C because the drawing’s dimensions were in millimeter too.
Since the dimensions and origin of the coordinate system of the AutoCAD drawing coincide with those in Sap2000 so we need to move vertically the arch up exactly 5.0m in X-Z plane. We can do this easily by using the Move command in the Edit menu.
11
Figure: The drawing can be moved 5 m in the Z direction. Step #4: After positioning the arch truss, we can draw the web members, chords, columns girders and purlins. Before that, define the cross section of them in terms of the material and dimensions. In this case we wish to use A992Fy50 type of steel as building material. The type and preliminary dimensions of parts of the building are as follows:
Web members: steel pipe with 150mm outside diameter and 3mm wall thickness. Upper and Lower chords: steel pipe with 150mm outside diameter and 3mm wall thickness. Columns: steel pipe 300mm and 5mm wall thickness Purlins: steel tube section with 80mm outside depth, outside width 40mm, flange thickness 2mm and web thickness 2mm. We can do this by following Define > Section properties >Frame sections >Add new property>pipe.
12
Table 1: The dimensions of parts of the frame in preliminary design
Purlin ( tube) outside depth outside width flange thickness web thickness
80mm 40mm 2mm 2mm
U & L chords and web members ( pipe) outside diameter Wall thickness
150mm 3 mm
Columns & Girder ( pipe ) 300mm 5mm
Step #5: Our aim in this step is to draw the web members on existing webs members drawn in AutoCAD. After drawing new web members, we should delete the old webs members. So select all the web members and then unselect all and then select “Draw Frame/Cable “command to draw web members. After completing the web members, delete the pre-existing web members by clicking on “Get Previous Selection” and then delete it consequently. Step #5: Draw the columns on the window of “X -Z plane @Y=0” Step #6: Delete the existing lower and upper chords and draw new chords using steel pipe with 150mm outside diameter and 3mm wall thickness. Step #7: Replicate the upper chord to both left and right side (dy= ±500 mm) and then delete the chord itself. Step #8: Select all the drawn web members and delete them. Step #9: Now start to draw the web members in 3D form. In other words, connect the web members in all three chords (one lower chord and two upper chords)
13
Figur e: The web mem bers can be thoug ht as set of triang les. The head s are conn ected at the lower chord while the bases are connected to each other at the upper chords.
Step #10: After drawing the 3D of one of the arches, then we can replicate it (dy=6m, number=6) Step #11:
At x-z plane @ Y=0, select all the joints on the arch and then extrude these joints to purlins. We can do this by following Edit >Extrude >Extrude points to frames/Cables (Property for added objects: Purlins, dy=5m, number=7). Since the length of each bay is 6m and distance between chords is 0.5m on each side then the length of each purlin is 5m in y-direction.
Step #12: Assign the restraints at joints on X-Y plane @ Z=0. Select the points of the joints and follow Assign > Joint > Restraints
Figure: Assigning joint restraints 14
CHAPTER FIVE 5.1 Analysis of Triangular arch truss Step #1: We have used A992Fy50 type of steel as our building material so far. We can change the properties of steel by following Define > Materials. (Steel grade A38, min yield stress=250 kPa, min tensile stress= 300 kPa) Step #2: In this step, we can define loads on the structure. To do so follow Define>Load patterns We can add Dead load, Surcharge (Super dead) Load and Roof live load. Step #3: Now we can have our load combinations. Follow Define>Load combinations and then select Add Default Design Combos and then select Steel Frame Design. Doing so, UDSTL1 and UDSTL2 will be added. Step #4:
In this step we wish to draw the girders connecting the columns. We can select ‘steel column pipe ‘and start to draw the girders on X -Y plane @ Z=5m. Step #5:
In this step assign the loads on the purlins. To do so select the all the purlins and then follow Assign> Frame Loads > Distributed. Add a 0.4 kN/m as a Surcharge load in gravity projected direction. Repeat the procedure for adding 0.7kN/m of roof live load.
15
Figure: The window can be opened after right clicking on one of the purlins
Step #6: Let’s start the analysis of the frame in this step. Follow Analyze> Set Analysis Options and choose Space Frame as our structure to be analyzed. After that, run analysis by pressing F5. Set the model to ‘Do not run “because we only wish to do a static analysis . Take your time until the computer is ready to show the analysis result.
16
Figure: The brief information after running the analysis
Step #7: After running the analysis you can see the deformed shaped of the structure under any type of load. Follow Display > Show Deformed Shape. From this window you can select the load combination or the type of load under which you wish to see the deflection of the structure. You can watch the behavior of the frame much better under, let’s say UDSTL2, by clicking on Start Animation.
17
Step #8: In this step, we can see the forces and stress on any member of our structure. For instance, we wish to see forces and moments on a joint under UDSTL2. Follow Display> show Forces/Stresses > Joints.
Figure: Right clicking on the joint will represent this window
In the same way, if we wish to see the axial forces in the members we can follow Display> Show Forces/Stresses> Frames/Cables/Tendons.
Figure: selecting any member and right clicking on it will show the internal reaction diagrams.
18
Figure: Diagrams for a column
CHAPTER SIX 6.1 Design of Triangular arch truss Step #1: We need to choose a design code and specifications for our structure. In this case, we wish to use AISC 360-10 as our design code. To do so follow Design> Steel Frame Design> View/Revise preferences.
19
Figure: Design code and specifications
Step #2: Add the design load combinations by following Design> Steel Frame Design> Select Design Combos. In this section add UDSTL2 along with UDSTL1. Step #3: Follow Design> Steel Frame Design> Start design/Check for structure Step #4:
20
We can revise the strength of steel in this step. Since our structure has excessively deformed, we increase the strength to min yield stress=250 MPa and min tensile stress= 300 MPa. To do so follow Define > Materials Step #5: In this step, we can revise the dimensions of parts of the structure set in the preliminary design. We can do this by following Define > Section properties >Frame sections >Modify /Show property
Purlin ( tube) outside depth outside width flange thickness web thickness
80mm 40mm 1.5mm 1.5mm
U & L chords and web members ( pipe) outside diameter Wall thickness
150mm 2 mm
Columns & Girder ( pipe ) 300mm 5mm
Table 6.1: The dimensions of parts of the frame in the final design
Step #6: Follow Design> Steel Frame Design> Start design/Check for structure. Now clicking on any member will show the results of the analysis. This thesis is going to be submitted along with results of analysis of members of the structure.
CHAPTER SEVEN 7.1 Summary The main object of this thesis is to show how to model, analyze and design an arch truss by using SAP2000. In the beginning of thesis, we discussed about SAP2000 and its capabilities in analyzing structures. Then, we explained the importance of trusses and in particular the arch trusses in steel structures. In fact, the combination of an arch with a truss system gives the building a powerful structural stability and strength to resist large loads and in turn handle their effects. The building material of trusses, which is mainly steel, is another advantage of these type of structures. However, there are some disadvantages of it as well yet it can be partially avoided with a smart and creative design of structure. The modeling of our industrial building starts in AutoCAD. After drawing an arch truss with given dimensions in AutoCAD we can easily import it to SAP2000 in order to complete the modeling process. The modeling process is explained step by step in order to show different features of modeling in SAP2000. It should be noted that some steps are prerequisites for some other upcoming steps of modeling. 21
The analysis of the building is another task when we are done with modeling. The analyzing process judges the model of the structure with regard to the dimensions and quality and its response to assigned loads and reactions in terms of internal reactions and deflection of the frame. Finally, the final design of the building can be done as soon as we have the results of the structure. The analysis and design of the building is also shown in steps. The analysis and design results are prepared in separate sheets so they can be attached to this thesis. Besides, the soft copy of the project is available in the following website address: https://www.dropbox.com/sh/4azmbmt5at2ynd0/AAC9k3ZWVqoGPIps7D5gtCqpa?dl=0 The model of our industrial building looks like the following figures.
Figure: The view of the building in X-Z plane
22
Figure: The view of the building in X-Y plane
Figure: The view of the building in Y-Z plane
23
Figure: The three dimensional view of the building
Figure: The view of a tr iangular arch truss: The Triangular shaped elements are connect by three curved chords in a zigzag form in order to construct a space frame truss of a triangular arch shape.
24
