Page 161 - Bridge and Highway Structure Rehabilitation and Repair

136 SECTION 2 STRENGTHENING AND REPAIR WORK

equations approach, it is mathematically convenient to assume Cartesian coordinates in
three dimensions.
2. By performing analysis, we translate the physical concept into a mathematical procedure
which serves as the basis of sizing the member or finalizing its design. It determines external

force effects on the structure, which for equilibrium is resisted by internal forces within the
material.
3. Stress resultants on a structural member can be idealized as bending moments acting in
two planes at right angles and a torsion in the third plane. Out of the three moments, one is
torsion and the other two are bending moments, all acting at right angles to each other and
located in planes at right angles.
Similarly, the shear forces acting in two planes at right angles and an axial force in the third
plane are complementary to each other. Out of the three forces, one is axial force and two are
shear forces, all acting at right angles to each other and located in planes at right angles. This
reference system in setting up a mathematical model is widely used in structural mechanics due
to its simplicity in locating moments and forces in a structural member.
It may be further noted that axial force can be compressive or tensile. Compressive force
may result in global or local buckling when compressive stress is very high. Tensile stress may
result in tearing of material due to direct tensile stress.
Magnitude and distribution of forces and moments can be analyzed by the following ap-
proaches:
1. Idealizing or selecting a structural behavior—Such as representing a straight line for a beam,
a convex curve for an arch, or a concave curve for a cable. The line element, whether straight
or curved, in each case can be assumed to act at the centroid of the cross section.
2. Mathematical model—Such as a thin plate as compared to a thick plate.
3. Reference system for measurements—Such as rectangular (cartesian x, y, z coordinates) or
curvilinear (r, 0 coordinates).
4. Analytical tools—Such as stiffness methods, strain energy method, or differential equa-
tions.
5. Numerical model—Such as solving a system of algebraic equations using matrix inversion,
iteration, or the step-by-step Gaussian elimination method.
6. Computational model—Such as programming computers with high speed, large storage
capacities, and virtual memory, which would enable solving a large number of unknowns
resulting from multiple load combinations or post-processing of results.
7. Manual computation methods—Such as checking computed results by empirical
methods.
A designer is also an analyst and must have a clear concept about the fundamentals of the
subject. Hence, to keep up with technological advancements, the knowledge base for applying the
principles and theorems of statics and dynamics to structural behavior needs to be supplemented
by continuing education or training courses.
4.2.3 Resistance to Applied Loads

Resistance can be defined as a resisting force or stress. It is the maximum quantifi able value
beyond which cracking or failure of material will occur. A bridge can only be insured if it meets
the legal requirement of Resistance 9 Applied load.
The three recognized methods of design are presented here. They evolved to meet society’s
need for a reliable infrastructure:
1. Elastic or working stress is the oldest method.
2. The load factor design (LFD) method served as an approximate ultimate load method. It

has now been replaced by the more refined LRFD method for highway bridges. For railway
and transit bridges, the LFD method is still being used.