Structural Analysis & Lateral Stability
So far in this series our structural analysis has focused on how vertical forces are transmitted from the point of application, through the structure, and back down to the ground via the foundations. Before we can wrap up the analysis of this bridge, we need to think about the lateral stability of the structure. It’s not sufficient to simply design a path for vertical loads to make their way into the foundations, we have to think about how any lateral loads would be transmitted through the structure also.
It’s true that in most cases the predominant loading direction will be vertical, however lateral loads can arise from a number of sources. The most obvious one is wind, probably followed by dynamic earthquake loading. Wind action on bridges is a fascinating topic in its own right, however wind won’t have a significant impact on this particular bridge as there’s not much surface area to catch the wind. Nevertheless, we still have to ensure the structure is robust. So wind or no wind, we need to tie the structure together and facilitate a safe transmission of loading in the out of plane direction (perpendicular to the span direction in the plane of the deck). In this post, we’ll carry out a brief qualitative (without numbers) structural analysis to demonstrate the load path providing lateral stability.
Looking at this bridge we can see a number of features designed specifically to provide lateral stability. To facilitate the discussion let’s assume a horizontal point load is applied half way up one of the vertical members. We can think of the vertical members (on the side of the bridge) as spanning between the deck and the top of the truss, let’s call it the ‘roof’ for brevity. Thus the applied force will be distributed via bending and shear equally into the roof and deck, as shown by the two blue force arrows in Fig. 1.
In Fig. 2 we can see that the wind truss in the roof (blue) spans between the frames (orange) at each end of the deck. These frames transmit the high level loading via bending and shear back down into the foundations. In this way, the roof (blue) and moment frames (orange) act together to provide a unified (side facing) ‘portal’ frame into which lateral loads can be transmitted and carried back into the foundations.
Taking a closer look at the wind truss in the roof we notice that all of the members are quite slender indicating they’re only designed to resist tension forces (they would buckle under any significant compression force). Looking at Fig. 3 we can see how the forces are transmitted through the truss.
Let’s say that the external loading is coming from the south (bottom of the figure). In this case tension is developed in half of the diagonal members as shown. In theory, compression forces would develop in the opposite diagonal members (shown with no force arrow). In reality they are so slender that they will simply sag under their own weight and continue to deflect under the action of any compression force. But, the existence of the tension members stops this from happening. The net result is that the tension members are facilitating force transmission through the truss and at the same time, protecting the opposite diagonal members from excessive deflection due to compression. The clever thing about this strategy is that if the external forces come from the opposite (north) side, the roles are reversed; the currently dormant diagonals go into tension, allowing the currently active members to simply sag under their own weight with negligible internal force developed. Any time you see cross bracing with very slender members, this is the strategy being employed.
The wind truss successfully channels forces to each end of the bridge. The next step is to get them down to the foundations. This is achieved using the framing action of the end-bay frames, Fig. 4. The term ‘framing action’ refers to the frame’s ability to resist lateral loading by developing internal moments and shear forces. The triangular arrangement of smaller members across the top of the frame in Fig. 4 are provided in order to stiffen the frame against lateral sway. Remember, the magnitude of lateral loads on the structure is expected to be small so we would not expect to see very stocky members provided. Note the ‘lever arm’ marked in Fig. 4. The larger this distance, the smaller will be the stresses developed as a result of the sway moment. Remember, moment Force lever-arm.
The last component of the lateral stability system to investigate is the bridge deck. The load that was transmitted into the deck is carried directly back to the foundations via the deck acting as a stiff diaphragm or plate. Cross bracing is not required in the deck (the way it’s used in the roof) because the deck timbers provide more than adequate stiffness to the deck in the out of plane direction. In the out of plane direction, we can think of the deck as a simply supported beam spanning 40.2 m with a depth of 4.9 m (deck width), Fig. 5. This would give a very favourable span/depth ratio of 8.2, well within the comfort zone for a simply supported structure.
That pretty much wraps up our structural analysis of the Fort Atkinson Truss Bridge. It’s worth recapping some of the main points from this blogtorial series. In part 1, we initially talked about the importance of recognising the differenced between structural models and real world structural behaviour. Remember, our models are only approximations of how we think the structure will behave – forget this at your peril! In part 2 we talked about the concept of a load path and how we need to clearly define and design load paths into our structures. We demonstrated some practical methods of load path analysis in part 3, namely the Method of Sections and Joint Resolution Method. In this final part of the series, we looked at the importance of facilitating lateral load transfer, i.e. providing lateral stability by transmitting lateral loads back into the foundations.
Hopefully you’ve found this case study analysis to be a helpful exercise. Why not try it again yourself with another structure. The next time you see an interesting structure, be it a bridge or building, take some time to dissect it and carry out a structural analysis. Try to work out just how it’s resisting the effects of gravity and all of the other elements nature throws at it! Spend enough time doing this and you’ll start to develop a strong intuitive understanding of structural behaviour.
As with all of my blogtorial posts, you can sign up to receive your PDF copy of this and future posts using the signup box below. If you want to brush up on your structural analysis skills, you can enroll in my free Fundamentals of Statics course. See you in the next post.