Saturday, February 5, 2011

The perks of 3D modeling...

Something about being able to turn a professor's 2D geometry with lots of labels and lots of trig equations into a simple 3D plot makes for a joyful Saturday afternoon homework session.

 Visualization is a critical component of Civil engineering. Being able to work with 3D data is an unspoken requirement in our field along with the ability to manually(and quickly) visualize the scale of dimensions.

With the Revit conceptual mass environment, one can easily play with 3D data and train the eye to better deal with 2D-3D coordination.

The problem itself was rather simple but I didn't have accurate notes so I had to patch up a numerical example to glean the geometric data:

I had a given set of equation and a badly drawn diagram; I had to deduce what angle alpha was referring to to. Given  the equation set below and the geometry below(my revit conceptual mass model), I had to find angle alpha. With the Revit drawing, it became clear what alpha was.( My notes didn't have alpha drawn on the diagram).
Fig 1.

Fig. 2

From the diagram it is clear that  Line AP is perpendicular to line OA therefore the length of OP can be found from a two consecutive application of Pythagoras theorem.  Knowing the length of AB and BP, AP can be find and hence angle subtended by OA and OP, alpha, can be found.

All this sounds elementary but bad note-taking had me reeling.

Friday, February 4, 2011

Calatrava's suspended structures: Force Equilibrium Analysis method

Indeterminate Cable stays

 In the Serreria bridge there are three points of resistance including two rollers at the ends of the bridge. At the junction of the deck and the pylon the connection is a fixed connection, hence the deck and pylon are monolithic.

The analysis of real cable-stay bridge from a system point of view requires a number of material science considerations in addition to the load path. These factors include creep(in the case of concrete) and temperature deformations.

As a result the final deformed state can be unpredictable and markedly different than the predictions based on mechanics alone. The structural engineer seeks an analysis method and sets of assumptions which will predict a "naturally/energetically" stable state of force distribution and deformations. This "stable state" is one that can "absorb" the effects of the elements on the material and overcome the material's degradation without redistributing the forces and deformations in an unpredictable manner.

Force Equilibrium method
The cable-stay bridge model(Fig. 1) in which the cable-deck junctions are modeled as simple vertical supports is considered both extremely stable and practical. In this manner the deck/girder is modeled as a continuous beam with rollers at the cable-deck junctions and a pin at the pylon-deck junction(Fig. 2). As such the bending moment profile of the continuous deck/girder can be used as a target to optimize the cable forces. Fig. 3 shows the tension forces acting on the deck and pylon at their respective junctions.(All drawings 1,2,3 are Autodesk Revit structure line models)

Fig.1 Revit Line drawing: cable-stay

Fig. 2. Equivalent continuous beam model of cable stay

Fig. 3. Tension forces at interface of deck and pylon

The practicality of modeling this behavior is where structural engineering struggled with. However, several approaches are now available.

The assumption of Fig. 2 is adequate for optimizing the cable forces from a strictly mechanics point of view. To account for creep and environmental deformations, appropriate pre-stressing and creep loading can be added to the model. Using Chen's method(referenced above) a Matrix equation can be set to iteratively find the optimum cable forces that will satisfy the Target bending moments in the deck/main girder which stabilize the system.

If  {M0} is the matrix of target Moments at the Cable/deck junctions, and [m] is a matrix of moment coefficients due to unit vertical point loads at the joints, {T} is a vector of optimum cable forces and {Md} is a vector of extra moments due to creep and prestressing and other environmental factors;

{M0} = [m]{T} + {Md} can be solved to find {T}.

The iteration comes into play if one chooses to additively account for the different factors that cause bending moments in the deck/girder.

In the simplified academic exercise, {Md} is {0} and {T} can be found easily.

Monday, January 24, 2011

Calatrava's suspended structures: Structural Analysis 1

The heart of structure behavior: LOAD PATH

 The load path is a term that describes the distribution of the loads within the structure to the reservoir of resistance(the ground). By the principle of conservation of energy, the load path is the path that minimizes the total potential energy of the system.

    Energy Analysis of Cable-Stayed Bridges

    J. Struct. Engrg. 112, 1182 (1986)

The brute analysis of a cable-stay bridge assumes that there is minimum(or zero) bending in the deck span. For analysis purposes this means that the cable-stay can be analyzed as a truss(i.e. all loading are transferred as point loads at the intersection of the cable and the deck/pylon.

I want to examine the natural load path with and without the assumption of truss behavior.

A cable-stayed bridge analysis is complex because
(i) it is 3D
(ii) non-linearity is possible.
To understand it at the fundamental level, I will use Staad.Pro models and Midas Civil 2011. My goal is to analyze and interpret the results of a structural model of the Serreria bridge by Calatrava. To accomplish this I modeled the bridge in Midas Civil(shown below). I then proceed to break down the behavior of the model from first principles.


Fig 1. My Midas Civil 2011 model of Calatrava's Serreria cable-stayed bridge

The load path of suspended structures, when fully understood, can help one to iterate between "form follows function" and "function follows form".


Fig. 2 Frame model of a suspension bridge system(modeled in

Natural Load Effects

In the figure below(Fig. 2), a series of joint loads are supported by a system modeled as a frame. Without releasing end moments in the inclined members or specifying those members as tension members,the load effects show all the possibilities of structural deformation. That is, the effect of the load on members include shear, axial, moment and torsion.

Fig 3: A highlighted suspension member(in red) without end moment releases exhibits moment and axial load effects. 

Load effects under constraints

When the inclined members are connected to the rest of the system by pin connections,those members behave like trusses(that is, there are no moment due to shear or torsion). Still, the beam and column continue to behave as beam-columns, exhibiting all the load effects due to the point loads imparted by the inclined members

Fig. 4 Far left suspension member in compression under conditions of end moment release. There is no constraint that the member can only carry tension.

It is instructive that at the location of the support(pin connection), the internal force in the suspension member is compression. That is, for linear analysis of a determinate truss, the member force at the support of a cable will be compression(this is valid under conditions where there is only gravity load as in the case of a cable-stayed bridge loaded under its own weight).

As shown in Fig. 5 below, when the suspension member is specified as 'tension-only' it is deactivated in the stiffness matrix of the system if it undergoes compression. The load transfer is iterated until the all tension members are either zero force members or are in tension. To avoid this iteration, a back-stay cable can be used to stabilize the system as shown in figure 6 below.


Fig. 5 Tension only member on left is deactivated in Staad because in the first iteration it experiences compression. (NB: all the cables are pre-tensioned with 1-kip force)

Fig. 6 Support back-stay cable ensures that all designated cable members(tension-only and pre-tensioned with 1-kip) are in tension in equilibrium. The main vertical member(pylon or tower) is connected to the main girder by a fixed connection. Rollers at the ends of the main girder allow horizontal movement.

 Fig 6. is the basic structural skeleton of Calatrava's cable-stayed bridge motifs. In the Serreria bridge, he ammends this motif by creating a curved pylon in place of the vertical to give it some dramatic feel.

Assumption of Minimal bending in deck span

In practical cable design, for optimal serviceability, bending in the deck is undesirable. This constraint can simplify analysis because the cables, deck and pylon(s) can be assumed to behave as trusses. Using this assumption increases the axial forces however, as shown in fig 7.

Fig. 7 The deck spans are modeled as truss members. The cables are also modeled as truss members. The pylon is left as a beam-column. The results of axial forces shows relative thickness of the axial force 'fills' . In this model, there is no pre-tension in the cables.

Wednesday, January 12, 2011

Calatrava's Suspended structures: Archs, Cables

I am reading Alexander Tsoni's book on Calatrava's bridges and wanted to discuss the structural behavior of Calatrava's different motifs for suspended bridges.

 Suspended structures as swing sets

When a child is suspended on a swing set, her weight is transferred into the supporting rope/cable/spring as tension. The tension then acts on the horizontal frame as downward point loads which are in turn carried into the vertical frame as compression loads into the ground.

The design of the suspension bridge is similar. The deck acts as the seat of the swing set, the arch or pylon as the frame and the cables act as the tensile element. With this basic design, the bridge can be designed with different configurations that act similarly.

Symmetric cables

Fig. Above: 3D view of Autodesk Revit Conceptual Model of Serreria Bridge(Click on picture to enlarge for all figures)

 The Serreria Bridge in Valencia, Spain is a motif that uses a symmetric pylon to suspend the deck and stabilizes the pylon with symmetric back stay cables. In this case the symmetry is achieved with one pylon in the spine of the bridge.

Structurally, the curvature of the pylon is optimized to resist the static forces in the span of the bridge. The angle of the parallel cables is optimized to resist the counter-forces  against the cable stays. Finally, the two back-stay cables provides additional stability to the pylon.

At both ends of the deck and the base of the pylon, foundation elements take the loads into the ground. At the abutments, rollers are designed to provide torsional support. At the base of the pylon, the connection is fully fixed by means of concrete box attached to the pile cap of the foundation element.

Fig. Revit Sheet showing interface of design software

Fig.Showing profile of deck new abutment.

Thursday, March 4, 2010

Leak-proof pre-fabricated architectural homes

One aspect of a prefab home that has irked me is the strong possibility that the joints in modules are the weakest points for both structural problems and livability/architectural problems.

In short how does one build a house within a few weeks(as most prefab architectural/engineering companies claim they do) without leaving holes that water, insects and air can filter through?

In prefab homes that use aluminum modular walls and floor systems, I've learned that most prefab companies use  high tech connectors designed to be air tight. One system I've discovered through reading the lines of prefab giant, Jeriko House is the use of a variant of T-slot framing common in industrial applications.

 In this approach, the main gravity/lateral system of the house is built with classic beam-column frames with attachment points that the floor and wall systems plug and play into.

Above, one can see the that the frame of the building at the corners show aluminum profile frames that the curtain wall and regular walls frame into. Source: Kieran Timberlake Associates

Above, the right wall clearly shows that there are metal(aluminum) channel tracks that walls frame into in a T-slot plug-and-play fashion.

More evidence of T-slot framing at the edges of glass walls and floor

The industrial modular building systems giant, PortaFab, uses this technology for designing quick-to-assemble clean rooms for manufacturing houses.  Using aerospace-grade aluminum a hollow channel with T-slot profile with thickness less that 0.1 inch is used to frame the main structural layout. The floor and wall systems then attach with precision to the frame.

 Source: PortaFab website

The corner framing is hollow to serve as mechanical and electrical conduits. Depending on climate needs, the floors or walls can also be hollow to serve as similar purpose. Backup wall elements(insulation, air/vapor barrier and stud framing) can be laminated to the aluminum panels as needed.

The sealant technologies used in this prefab modules are patented so I have no clue what the design is made of. The building envelope design guide(from Whole Building Design Guide(WBDG)) gives guidelines on different options for joint detailing depending on whether or not the metal panels are rain-screened system or barrier system.

This is my amateur attempt at detailing an aluminum track for prefab walls in Autodesk Revit:

Friday, February 19, 2010

Solar Town - Krofa Project

Here's a preliminary view of site in revit

The Krofa Project is a town development plan that uses a virgin 10 million sq. ft. area to develop a sustainable suburb that is home to workers at a pre-fabricated house factory nearby. The project is inspired by the K.N.U.S.T campus plan in Kumasi, Ghana. Krofa is unique, however, because in addition to smart transportation plan of the area , the domestic energy base is served by passive sustainable design that optimizes natural light and cooling/heating. In addition there is design to optimize rainwater use during rainy season.

The structural/architectural work-flow is as follows:

(i) Preliminary Google Earth surface/image use in AutoCAD Civil 3D
(ii) Road alignment creation and profile and corridor/corridor surface creation in C3D
(iii)Integration of C3D with Revit Structure
(iv)Road/Street Layout in Revit
(v)Solar/Light/Shadow studies of house layout on residential site with conceptual house models inAutodesk Ecotect
(vi)Architectural design of factory and homes
(v)Structural design of all structural components

To be continued... I'm quite hungry. lol

Below:  A house begging for a tropical landscape.

Friday, February 12, 2010

Draping Colored Google Image over Google Surface/Contour data in AutoCAD Civil 3D

Newbies to Google Earth(GE) surfaces/images in AutoCAD Civil 3D are disappointed to realize that the images imported using the GE Importer are greyscale.
The preliminary solution to this problem is to
a. save the Google image directly from GE into a folder
b. next, attach the image into C3D
c. next drape the image unto the surface.

But there's a catch. If you want to certify that your image and surface are aligned properly and scaled equally, you have to make sure that your coordinate systems for importing Google earth data and attaching external references are the same.

Google Earth by default uses the coordinate system of the image/surface location so no matter what coordinate system you drawing settings are set to in C3D, it will import the image/surface at the locations set in GE.

Equally, external references use the coordinate system set in the drawing settings. So if you mistakenly set the coordinate system to different zone that the location of the imported GE image/surface, you'll find out that there will be an XY scale error when you attach the colored image saved from GE.

I found out that when I manually enter the coordinates of both the Google Earth image/surface and the attached colored GE image there is no alignment offset.

This video illustrates it. The video shows two different drawing settings with two different drawing coordinate systems. Click on link below to see video.


Finally this is a video of the cool 3D view of colored Google image draped over the 3D surface of the site.