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CHAPTER 4                         AN ANALYTICAL APPROACH TO FRACTURE AND FAILURE            169



                                                            x No. of lanes
            : L/1000. L     pedestrian/No. of beams 4    vehicle
                                                            No. of beams
        6. For vehicular loads on cantilever arms, maximum computed defl ection : L/300.
        7. For vehicular and pedestrian loads on cantilever spans, maximum computed defl ection is
            25 percent lower, i.e., : L/375.

        8. Deflection check is optional in current AASHTO LRFD code.

        4.13  REVIEW OF COMMON FAILURE THEORIES OF MATERIALS
        4.13.1  Failures Related to Construction Materials
            In Chapter 3, external reasons for failure were based on:
        1. Design defects such as incorrect assumptions, error in data, incorrect analysis, non-compli-
            ance with code guidelines, incorrect connection details, and mistakes in drawings.
        2. Construction defects such as poor workmanship, substandard materials, inadequate concrete

            curing, imperfections in steel, lack of fit, and lack of quality control.
        3. Investigating probable modes of failure: The response of materials to external forces like
            steel and concrete is discussed here.
            Postmortem of collapse reveals details of sudden or progressive collapse. Large displace-
        ments result in combined shear and bending type overstress in members.
            Critical sections for plastic hinges to form are located at midspan, under the concentrated
        load where deflection or positive bending moment is highest, or at a support where shear force,

        reaction, or negative bending moment is the highest. Tension yielding occurs in the fl ange.

        4.13.2  Modes of Failure for Steel Bridges:
        1. Bending tension stress in a member is exceeded due to long-term fatigue.
        2. Shear stress or principal tensile stress is exceeded at girder supports.
        3. Failure of bolts or welds at joints.
        4. Local buckling of compression members.
        5. Increased thermal stress in members due to malfunction of bearings.

        6. Foundation movement due to flood scour during floods leading to settlement of pier

            or abutment.
        7. Settlement of pier or abutment due to liquefaction during earthquake.
        8. Lack of adequate support width at abutment during earthquake.

        4.13.3  Review of Leading Theories of Yielding of Steel
        1. When a specimen of steel is subjected to increasing axial load, a point is reached when axial
            stress is no longer proportional to strain. Hooke’s Law is no longer applicable and the material
            is said to be yielding. Ductile metals like steel exhibit yielding and subsequent plastic defor-
            mation. Theories of yielding based on principal stresses and strains are summarized here.
        2. Von Mises shear strain theory which is based on principal stress difference is most accurate
            and correlates best to experimental behavior.
        3. Tresca maximum shear stress theory gives reasonable predictions and has a simpler math-
            ematical form.
        4. Rankine criteria for maximum principal stress: When a point in a material is subjected to
            principal stresses in three directions, yield of material will occur under the maximum of the
            three principal stresses for applied tension.
              As an alternative, yield of material will occur under the minimum of the three principal
            stresses for applied compression.
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