Forward Analysis for a Cable Stayed Bridge

Vinayagamoorthy Marriap Sr. Technical Support Engineer, MIDAS R&D Centre, Mumbai

Overview

In general, to design a cable-stayed bridge, a final system (completed system) analysis and a construction stage analysis are required. From the final system (completed system) analysis, dimensions of a structure, cross section of cables and cable forces are determined.

Depending on the erection method, the structural system of a cable-stayed bridge can be changed greatly. And the change of structural system can cause an unstable state during construction. In this regard, construction stages should be composed in a way that the construction stages, which affect the structural system, are included and should be used to check the structural safety. When the analysis is performed following the erection sequence to fulfil this purpose, it is called Forward Analysis. Through the forward analysis, stresses in construction stages, construction sequence and possibility of construction can be checked and an optimal construction method can be selected.

The reason for being difficult to apply forward analysis to a cable-stayed bridge is that the cable forces to be introduced at each construction stage are hard to know. In Korea, most of cable-stayed bridges have been designed by using backward analysis followed by forward analysis. From the backward analysis cable forces were determined, and afterwards using these cable forces the forward analysis was carried out.

Forward Analysis for a Cable Stayed Bridge
In this case, the structural systems between backward analysis and forward analysis are different and therefore, key segment closure is different between the two analyses. This leads to the fact that the final member forces at the final stage from the forward analysis are different from the member forces from the initial equilibrium state analysis (at the final system (completed system)). In the initial equilibrium state analysis for the final system (completed system), after the self-weight of the structure, cable forces and superimposed dead loads are applied to the key segment, the member forces at the key segment are calculated. However, in the forward analysis, the girder is deflected by its self-weight and cable pretension at the stage immediately before the key segment closure. When the key segment is closed, it is not affected by the self-weight of other structural elements except for the key segment itself and cable pretension. These differences from different structural systems lead to the differences in analysis results.

This problem is caused by not understanding the cable theory or by no existence of software taking care of this problem except for the software dealing with large displacement.

But the above mentioned is unreasonable according to the following reasons:
  1. Within elastic range, forward analysis result is the same as the backward analysis result. (e.g., not considering time-dependent effects).
  2. If the key segment closure force is calculated, both forward and backward analyses will have the same result as that from initial equilibrium state analysis.
According to the cable theory, unstressed length of cable is calculated by the initial equilibrium state analysis, and in backward analysis the cable length changes as the structural system changes and accordingly cable force changes with cable length. Therefore, if the planned construction stages are applicable to the design, it is also possible to achieve the aforementioned with forward analysis. First, unstressed cable length is calculated based on the cable force from the final system (completed system) and cable forces for each stage can calculated by considering the cable length changes with construction stages. However, until now this theory has been feasible only with large displacement analysis. It is because when the cable is installed by the cantilever method the cable length should be a real displacement. In a large displacement analysis, a newly created member can be installed tangentially to the existing member. Tangent displacement is referred to as a virtual displacement. But in a small displacement analysis, it is difficult to calculate the cable force considering the virtual displacement. However, in midas Civil software, even in a small displacement analysis, a virtual displacement can be considered. Therefore, if the unstressed length is computed and thereafter the forward analysis is carried out, it is possible to perform construction stage analysis with forward analysis alone. 'Lack-of-Fit Force' function converts the relationship between the unstressed length and the cable length into pretension loads so as to calculate the cable forces for each construction stage. As long as 'Lack-of-Fit Force' function is used, it is possible to analyze staged construction with forward analysis alone without backward analysis.

'Lack-of-Fit Force'(LFF) signifies 'Additional Pretension', which is introduced during the cable installation where the change of structural behavior and structural system are considered, or 'Pre-applied Force', which is pre-applied to the key segment so that the key segment can be located at the same position as the completed system when the key segment is to be closed. During the forward analysis, if the program calculates the 'Lack-of-Fit Forces' for the cable and key segment elements and these 'Lack-of-Fit Forces' are reflected in the installation of cable and key segment, the final stage result from the forward analysis will coincide with the result from the initial equilibrium state analysis.

Test Model (3 span cable stayed bridge)

Forward Analysis for a Cable Stayed Bridge
For a real design of a cable stayed bridge, connection of key segment and generation of side span supports, temporary bents, temporary rigid link between tower and girder and elastic link between tower and girder, which are the factors affecting the structural behavior, should be included. The forward analysis using Lack of Fit Force should be evaluated on various structural cases in order to be used for a real bridge. Therefore, before we apply forward analysis using LFF to a real bridge, we will verify the applicability of LFF function by performing the forward construction stage analysis for a simplified bridge, which includes key segment closure, boundary condition change during construction stages and installation and removal of temporary bents.

Test Model is a 2D 3-span continuous symmetrical cable stayed bridge. The total bridge length is 170m (40+90+40). The 8 cables are supporting the bridge.

Forward Analysis for a Cable Stayed Bridge
The "Backward Forward" results were obtained like this; first, cable force for each stage was obtained from backward analysis and the cable pretension was introduced as External Type Pretension for forward analysis. To consider the effect of key segment, LFF was applied to the key segment (beam) element.

As seen in the results, when the forward analysis without considering LFF is used (and the cable force for each stage is calculated by backward analysis), less cable pretension than it should be introduced, so the displacement at the final stage is greater than the displacement from the initial equilibrium state analysis and the cable force is smaller as a whole. Likewise, girder has the greater positive and negative moments than those from the initial equilibrium state analysis. On the other hand, when the forward analysis using LFF is used (and the cable force is calculated from the initial equilibrium state analysis), the displacements at tower and girder, the girder moment and the cable force are the same as those from the initial equilibrium state analysis.

Forward Analysis for a Cable Stayed Bridge
When LFF is considered for Truss only, both ends of the key segment are deflected upward at the stage immediately before the key segment closure. Since the key segment is closed from the position, large upward deflection results in at the final stage.

Conclusion

Forward analysis is carried out following the construction sequence and backward analysis is performed by removing structural members step by step from the completed system. Up to now, after initial equilibrium state analysis (at completed system) has been performed, backward analysis has been performed to find the cable forces for each stage and then based on these cable forces forward analysis has been performed. However, backward analysis is inconvenient compared to forward analysis and time dependent effects cannot be reflected in the backward analysis. According to the cable theory, forward analysis and backward analysis give the same result within elastic range as long as the unstressed cable length are obtained from the initial equilibrium state analysis (at completed system). In this test model case, we have seen that it is possible to analyze a cable stayed bridge, using Lack of Fit Force function, by forward analysis alone without backward analysis.
Trimble's software solution for motor grader, compactor & paver
Trimble, a global leader in construction technology, unveiled its platform-based software solution to assist contractors in improving the efficiency of their on-site equipment/fleet, especially motor graders, compactors, and pavers

Read more ...

Construction Technology For Speed, Efficiency, Resilience and Durability
Disruptive technology is reshaping construction practices from design and planning to project execution and facility management. The integration of cutting-edge technologies such as Building Information Modelling (BIM), 3D printing, robotics

Read more ...

Reliance ReRouteTM Turns Plastic Waste Into Road Construction Material
Roads constructed using waste plastic have higher durability, more resistance to deformation and to water induced damage, and improved stability and strength. ReRouteTM is an initiative for End-of-Life Multilayered Waste Plastics for Road Construction

Read more ...

Tech-Enabled Startups Redefining India’s Construction Industry
In the vast landscape of India’s construction industry, a new wave of disruption is sweeping through, powered by the innovative prowess of tech-enabled startups. These visionary companies have set their sights on transforming the way buildings are designed

Read more ...

Buildo.Market: Construction Materials Marketplace Using VR & Catalogs
The idea behind Buildo.Market is to provide a one-stop solution for construction-related materials and services in India, driven by the changing customer purchasing behavior during the pandemic. Previously, people hesitated to select materials without

Read more ...

Elixia's Technology Delivers Logistics Efficiency, Saves Time & Money
An efficient logistics system is an interplay of technology, infrastructure, and manpower and we are currently lagging in all these factors. The logistics sector is the backbone of economic growth; its efficiency has a direct influence on the growth of other

Read more ...

Find Skilled CE Operators, Manage Equipment & Cut Costs: EQUIP9™ App
EQUIP9™ - the first global start-up in the heavy equipment- aims to connect every entity in this industry and simplify the complex construction business with its app-based digital solutions. Find certified operators, manage equipment, and cut costs

Read more ...

Onsite Construction Management Software: Smooth Project Operations
In around 2 years, over 100,000 construction businesses in India have transitioned from their traditional methods to adopting Onsite, a tech-enabled startup that is disrupting the country’s construction industry by providing a range of benefits such

Read more ...

PACE Robotics' Modular Wall Finishing Robot: Save Time, Cut Costs
Robots offer a remarkable advantage, being able to accomplish tasks with a speed ten times faster than traditional methods, while also reducing costs by threefold. Moreover, they guarantee consistent quality, eliminate physically demanding

Read more ...

Powerplay Cloud-Based Construction Management Platform
With a rising level of digital literacy, numerous startups are developing cutting-edge solutions to address the challenges faced by the construction industry in India. Powerplay is a cloud-based construction management platform that helps construction

Read more ...

TappetBox's Data Capture Solutions Streamline Construction Workflow
TappetBox was born out of the realization that the construction industry lacks modern frameworks for data capturing and maintenance, particularly in equipment monitoring and management. TappetBox App helps construction companies collect, track & manage

Read more ...

Prabh Paul - Tracecost
Surging demand for prompt project delivery is driving global infrastructure towards automation, but India’s industry lags behind in adopting automated processes. Tracecost offers an innovative solution to address this gap, providing remarkable benefits

Read more ...

Roadmap for Innovation & Digital Tech Transformation in the Construction Sector
In recent times, companies, including construction firms, have become more enthusiastic about adopting disruptive new tech tools and embracing digital transformation. Despite various challenges, the accelerated digital evolution aided by investments

Read more ...

Harnessing the Potential of 3D Printing with Geopolymer Technology
The amalgamation of geopolymer technology with 3D printing gives birth to a method of construction that is both sustainable and efficient; it marries the speed and flexibility of 3D printing with the environmental and structural benefits of geopolymer

Read more ...

How Construction Industry is Using Technology to Become More Sustainable
Global warming and climate change are among the biggest challenges of our generation today. Almost 40 percent of energy-related greenhouse gas emissions are from the construction sector, as per UN’s 2019 Global Status Report for Buildings and Construction

Read more ...

Cusmat: Offering Immersive Learning Techniques
Cusmat’s Metaverse-based training and upskilling tools for technicians and operators in Mining, Logistics & Manufacturing industries are making training and recruitment more efficient, faster, and cost-effective. Cusmat is providing virtual reality or augmented

Read more ...

Driving Efficiency & Productivity with Smart Construction
As construction projects become more complex, construction companies must infuse agility into their operations to avert time and cost overruns by tapping into the benefits of advanced technology solutions like Building Information Modeling

Read more ...

Technology Boosting Jobsite Connectivity
While jobsite connectivity is making sure that information is transferring to the right individuals at the right moment so that they can do their jobs more effectively, however, executing jobsite connectivity is a completely different matter as every

Read more ...

Robots in Construction
Adopting Robots in construction can help maintain productivity at a time when fewer people are pursuing a career in the industry: GlobalData. The construction industry’s lack of digitalization and new technologies mean that companies will struggle to

Read more ...

Predictive Analytics is at the heart of Digital Transformation in the Energy Industry
Senthilkumar Pandi, a Digital Data Management expert, explains how Predictive Analytics enable the Energy Industry to prevent costly and unexpected downtimes, and suggests how to choose the right solution.Though digitalization has been

Read more ...