This chapter discusses system analysis in bridge design. It covers breaking bridge systems into subsystems and components for analysis, the importance of modeling assumptions regarding equilibrium, compatibility and material properties, and understanding the limitations of models. Safety of methods is also discussed, including establishing equilibrium, stress reversal, repetitive overloads, shakedown and plastic collapse loads, and fatigue. The relationship between modeling and design is summarized.

1. Summary of Chapter 10
System Analysis in Bridge Design
Prepared by:
Mahesh Pokhrel
International Student
Master’s in Civil Engineering, UTRGV
SID: 20585287

2. 10.1. Introduction
10.2. Safety of Methods
10.3. Summary
Contents of Chapter 10

3. 10.1. Introduction
To design any complicated systems such as bridge, we need to break the whole part
into smaller, more manageable subsystems or components.
• Subsystems include:
superstructure, substructure, and foundation.
• Components include:
beams, columns, deck slab, barrier system, cross frames, diaphragms, bearings,
piers, footings etc
• According to the AASHTO Specification, Design should be performed on a component
basis. Therefore, the engineer requires procedures to determine the response of the
structural system and ultimately its components.

4. 10.1. Introduction
• The distribution of the loads throughout the bridge requires equilibrium, compatibility, and that
constitutive relationships (material properties) to be maintained (basis for all structural
analysis).
• Equilibrium (static balance), Compatibility (internally consistent deformations) and Material
properties (properly characterize)
Typically, the assumptions that are made regarding these three aspects of analysis determine the
complexity and the applicability of the analysis model.
For example, a simply supported beam can be modeled by considering one dimensional equation;
𝑑4𝑦 / 𝑑𝑥4 = 𝑤(𝑥) / 𝐸𝐼(𝑥)
Several important assumptions were used for this mathematical equation. Such as: the material
behave linear elastically, the strain (and stress) due to flexural bending is assumed to be linear, the
loads are concentrically applied without torque, and finally, the beam is proportioned and laterally
braced so that instability (buckling) does not occur. (often these conditions do not truly exist)
Contd….

5. 10.1. Introduction
• The purpose of above simple system is to illustrate the importance of the modeling
assumptions, and their relevance to the real system. Engineer’s responsibility is to
understand the assumptions and their applicability and should take precautions to
ensure that the assumptions are not violated or that the consequences of the violations are
understood and are acceptable. When the assumptions do not adequately reflect the
behavior of the real system, the engineer must be confident in the bounds of the
error induced and the consequences of the error. So, it is impossible to exactly
predict the response of any structural system, but predictions can be of acceptable
accuracy.
• Whatever the mathematical model may be, the basis for the model and the
behavior it describes must be understood. (Approximations exists)
• Many parameters are difficult to estimate and in such cases, the extreme conditions (upper
and lower bounds) can be used to form an envelope of load effects to be used for design.
Contd….

6. 10.2. Safety of Methods
• It is important for the engineer to understand the limitations of the
mathematical and numerical models and the inaccuracies involved in the design
process.
• As models are estimates of the actual behavior, it is important to clearly
understand the design limit states and their relationship to the modes and
consequences of failure.
1) Equilibrium for Safe Design:
An essential objective in any analysis is to establish a set of forces that satisfies
equilibrium between internal actions and the applied loads at every point.
2) Stress Reversal and Residual Stress:
3) Repetitive Overloads: As the vehicular loading of a bridge is repetitive, the
possibilities of repeated loads that are above the service level are likely and their
effects should be understood.

7. 10.2. Safety of Methods
• The load above which incremental collapse occurs is termed the shakedown load . If
the load is below the shakedown load but above the load that causes inelastic action,
then the structure experiences inelastic deformation in local areas. However, after a
few load cycles, the structure behaves elastically under further loading.
• If the load exceeds the shakedown load (but is less than the plastic collapse load),
then incremental collapse occurs. if the load exceeds plastic collapse load, then the
structure collapses.
• Two theorems have been developed to determine the shakedown load: the lower
and upper bound theorems. These theorems help to relate the elastic behavior to
the inelastic behavior so complex systems can be analyzed without an incremental
load analysis. (This limit state is termed as incremental collapse)
4) Fatigue and serviceability: repetitive truck loads create fatigue stresses that may
lead to brittle fracture under service level loads.
Contd….

8. Relationship
of Modeling
to design

9. 10.3. Summary
This chapter gives the concepts involved with
the plastic and shakedown limits and how they
relate to the AASHTO design specification
(based on elastic analysis).
The process and flow chart of modeling
and design of bridge system