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## Guide for Heat-Straightening of Damaged Steel Bridge Members

### Chapter 6: Heat Straightening Rolled Shapes

#### 6.1 Fundamental Damage Patterns

The process of heat straightening damaged rolled shapes is based on a logical extension of the straightening of plates. Rolled shapes can be viewed as an assemblage of flat plate elements. When damaged, some elements are bent about their strong axis, some about their weak axis and some about both. The overall effect on a member results in damage which is a combination of one or more of the fundamental damage categories described in Chapter 1.

To develop a methodology for heat straightening complex damage on rolled shapes, understanding the behavior of such shapes when subjected to single fundamental types of damage is necessary. Focusing on categories S and W, a distinction will be made between a cross sections’s primary elements and stiffening elements. The primary elements are the plate elements subjected to bending about their local strong axes. The stiffening elements are perpendicular to the primary elements and bent about their own local weak axes.

For example, consider the channel shown in Figure 40, which has been plastically deformed about its major axis, resulting in Category S damage. The web of this channel, a plate element bent about its major axis, is therefore a primary element. The two flanges are bent about their minor axes and are thus stiffening elements.

For rolled shapes with flexural damage, the pattern of yielding usually differs for the primary and stiffening plate elements. Typically, the primary plate elements develop plastic hinges, a state of stress in which the entire cross–section has reached yield (F_{y}): Tensile yield in one region and compressive yield in the other.

The stiffening elements of a damaged rolled shape may exhibit one of several conditions. In the first, yielding does not occur because the stiffening element is located near the neutral axis of the cross section, e.g., when a wide flange beam is bent about its minor axis, the web may not reach yield. In the second case, the stiffening element is located near the extreme fibers of flexural yielding (such as the flanges of the channel shown in Figure 40). In this situation the flanges yield due to axial stress (either tension or compression). In the third case, the stiffening element is yielded in weak axis bending in which a region of yield is formed as shown in Figure 41. The results are a narrow strip of flexural yielding often referred to as a yield line.

**Figure 40. Primary and stiffening plate elements for a channel bent about its major axis (Category S damage).**

With the various patterns of inelastic deformation which occur in damaged rolled or built–up shapes, the heating pattern for repair must be tailored to fit. While the vee heat is generally used on primary elements of a section bent about their major axes, the stiffening elements may require a strip heat, line heat or no heat at all. Multiple heating patterns introduce additional variability, so the time to complete a heat may be considerably longer than heating a single plate. Considerable cooling may occur at the initial heating locations before the last element is heated, retarding expected movement due to increased internal restraints. A good practice to minimize the heating time is using more than one torch for complex patterns.

In addition to the jacking force factor, the various combinations of plate elements found in structural steel shapes introduces two other parameters that may affect the member’s behavior during heat straightening. The first is a shape factor and the second is a stress factor. It is obvious that the shape may influence behavior, but the stress factor requires an explanation.

When jacking forces are applied prior to heat straightening, the distribution of stress over the heated section due to jacking will vary according to the shape of the cross section and the restraint conditions. As the torch moves over the section, the steel temperature rises and then falls in a manner somewhat analogous to a wave moving across calm water. The heat variation produces continuous and complex changes in the combined stress distribution. As a consequence, stress distributions may be quite different between two members of different configurations.

**Figure 41. Weak axis bending resulting in a yield line in the plate element.**

One measure of this effect is the ratio of plastic moment, M_{p}, to the moment at initial yield, M_{y}. For a constant yield stress this ratio is Z/S where Z is the plastic section modulus and S is the elastic section modulus. Since the moment due to jacking is usually expressed as a percentage of M_{p}, the degree of yielding during heating is often a function of this ratio. For example, Z/S = 1.5 for a rectangular plate and is only about 1.12 for typical wide flange beams. In other words, yielding is initiated at two–thirds of ultimate capacity for a plate but does not occur until 90 percent of capacity for most wide flange members. For a moment due to jacking in the range of 35–50 percent of M_{p}, some localized yielding will occur during heat straightening. The amount, and consequently the degree of straightening, will depend on the stress factor as a function of Z/S.

The model for predicting movement during heat straightening is a modification of the plate equation, Eq. 5.3. For mild steel, the equation for plastic rotation of a structural shape can be expressed as

(Eq. 6.1)

where F is the factor associated with the external jacking force, F_{s} is a factor reflecting the shape of the cross section, F_{a} is the stress factor, and φ_{b} is the basic plastic rotation factor derived for a rectangular plate (see Eq. 5.3) and expressed as:

(Eq. 6.2)

The stress factor can be written as

(Eq. 6.3)

Where Z/S is the ratio of plastic to elastic section modulus for bending about the major axis (except for angles in which the ratio is multiplied by F_{s}).

The jacking force factor is identical to that developed for plates, that is

(Eq. 6.4)

The shape factor is

(Eq. 6.5)

Where

b_{s} = width of stiffening element;

d_{s} = distance from apex of vee heat on primary member to intersection of stiffening element; and

d = depth of the vee heated elements (assuming a vee depth (d_{s}) of at least three–quarters of this depth).

#### 6.2 Composite Deck–Girder Bridges

Two primary parameters affecting heat straightening—vee angle and heating temperature—have been discussed in previous chapters. However, three additional parameters have also been shown to play a central role in the heat–straightening process. One factor relates to the influence of restraining forces, a second to the heating patterns used, and a third to the damage–induced pattern. A typical damage pattern is shown in Figure 42. Typically, a lateral jacking force is applied to the lower flange during heat–straightening repair. However, the determination of the jacking ratio is complicated for composite girders due to the internal redundancy of the system. First, when a lateral jacking force is applied to the lower flange, only a portion of that force produces a moment in the flange. Part of the force follows a load path through the web into the upper composite flange and is resisted by the concrete deck. The determination of the actual moment in the lower damaged flange is required to prevent over–stress during jacking and to predict the expected movement. Second, the moment capacity due to a laterally applied load is also influenced by the load path transfer making it difficult to compute the plastic moment capacity, M_{p}.

The most effective combinations of heating patterns and restraining forces are ones that minimize any internal constraints inhibiting the straightening while maximizing the positive external constraint effect. For any damage condition, an analysis of these factors is required to optimize straightening effects. For Figure 43, the wide flange can be analyzed in terms of its web and bottom flange plate components as interacting elements.

Each has plastically deformed so attempting to straighten the first component independently of the second leads to the second component acting as a negative constraining force rather than a positive one.

**Figure 42. Typical deformed shape and yield zones in damaged composite girders.**

**Figure 43. Heating patterns for composite girder.**

##### 6.2.1 Factors Affecting Heat–Straightening Behavior of Composite Girders

###### 6.2.1.1 Heat Patterns

The term “heat patterns” refers to the combination and layout of vee heats, line heats, and strip heats used to conduct the heat–straightening repair. Conceptually, vee heats are used to repair plate elements with plastic bending about the major axis, while line heats are applied to repair plate elements with flexural damage about the minor axis. Hence, a vee heat on the bottom flange in conjunction with a line heat on the web, applied to their respective plastically yielded portions, are the proper heat patterns to repair a composite beam in Figure 43. Care must be taken to iteratively adjust the span of the line heats, so only portions of the web are heated that show plastic curvature after the previous heating cycle. Similarly, the vee heats are confined to the portion of the bottom flange with plastic deformations.

In addition, a half–depth web strip heat is usually required. The purpose of this heat is to reduce the differential shortening between web and flange. By heating the web with a half–depth strip, the web can deform and relieve some of these stresses. The strip heat tends to reduce the buckling of the web near the center of damage.

###### 6.2.1.2 Residual Moments

A characteristic of each damaged girder is the presence of residual moments. When damage is induced, the web acts as a spring resisting the movement. While a yield line typically occurs near the top of the web, there is also an elastic component of stored energy, often referred to as internal redundancy. During the first heat cycle, this restoring force acts as an additional jacking force tending to straighten the girder. Unless the external jacking ratio is reduced, the plastic rotation during the first heat cycle is magnified. The initial plastic rotation relieves the majority of this stored force, so, it doesn’t influence successive heats. If the girder is externally indeterminate in the impact direction, residual moments are also created during the damage phase. For either case this behavior should be considered when developing a constraint plan. A reduced jacking force is recommended during the first two heating cycles to minimize internal force effects and the possibility of cracking.

###### 6.2.1.3 Restraining Forces

The simplest way of providing restraining forces is to allow the unheated portion of the member to restrict thermal expansion by suitable heat pattern locations. This is a form of an internal constraint. Internal constraint may also be imposed by the self–weight, axial loading, or static indeterminacy of the member. Frequently, external restraining forces are used to complement or even negate the internal constraints to enhance the heat–straightening.

###### 6.2.1.4 Stiffening Effect of Web

When a lateral restraining force is applied to the damaged lower flange of a composite girder, the purpose is to generate a restraining moment in the lower flange. Due to the web interaction between the lower flange and the completely restrained upper flange, some of the applied force is transferred through the web into the deck rather than into the lower flange. For deep girders most of the force goes into the lower flange. However, for more shallow depths, an increasing amount of the force does not go into the lower flange. Only the fraction of the total force that is directly carried by the bottom flange provides external restraint to the vee heat. Hence, a jacking ratio assuming that the lower flange provides the total resistance does not reflect the true bending moment in the bottom flange and may be considered only as a nominal jacking ratio. It is more relevant to calculate the jacking ratio using the actual bending moment transferred to the bottom flange. This ratio is the effective jacking ratio.

##### 6.2.2 Model for Heat–Straightening Response

Avent and Mukai (1998) developed a model to determine the amount of the applied lateral jacking force that is actually distributed to the lower flange as opposed to that which is transferred through the web to the composite deck. The stiffness of the system includes both the effect of the lower flange and the web stiffening effect due to connectivity with the upper composite flange. Thus, only a portion of the moment generated by the jacking force (effective jacking force) is actually distributed to the lower flange.

The equation for the change in angle, φ_{c}, due to a single vee heat on the lower flange is

(Eq. 6.6)

Where

(Eq. 6.7)

(Eq. 6.8)

(Eq. 6.9)

(Eq. 6.10)

and d/t_{w} is the web depth–to–thickness ratio, M_{j} is the jacking moment if the lower flange carried the load independently of the web (apparent jacking force), and M_{p} is the plastic moment of the lower flange.

##### 6.2.3 Modeling Statically Indeterminate Spans with Intermediate Diaphragms

Practically all steel spans over roadways have intermediate diaphragms. When the lower flange is impacted, its behavior resembles that of a beam continuous over several supports with the diaphragms acting as these supports, Figure 44a. The impact usually produces a plastic hinge mechanism as shown in Figure 44b. The three plastic hinges produce reverse curvature bending and yield zones at the impact point and adjacent supports a shown in Figure 44c. The vee heat patterns are also shown in Figure 44c. Both the positive and negative curvature sections should be heated either simultaneously or in quick succession so rotation will occur at all three locations with reduced restraint from adjacent plastic hinges. Consequently, the model for the single span case should provide a reasonable approximation of this more complex situation. Important considerations for composite girder repair are the residual stresses induced during both the damage and the repair phase.

**Figure 44. Diaphram stiffened composite girder**

#### 6.3 Trusses and Axially Loaded Members

##### 6.3.1 Introduction

The stress condition of a member plays a major role in its behavior during heat straightening. In some cases the loads on a structure can be reduced to the point that member stresses are a minor factor. But for other cases, even after the removal of live loads, the dead loads produce significant stresses. A primary case in point is the truss bridge. Typically, the dead load stresses on such structures may range from 25–50 percent of maximum service load stresses in some members. It is thus necessary to examine the stress distribution of a structure prior to initiating heat straightening.

For the beam shown in Figure 45, dead loads produce bending about the minor axis of the wide flange beam. The dead load can have a neutral, positive or negative effect on repairs depending on the type of damage. For example if the damage is a result of bending about the beam’s major axis in Figure 45, but dead loads produce moments about the minor axis, a web vee heat is in a region of nearly zero dead load stress based on the original cross section. The dead load stress will have little effect on movement about the major axis after heating. If the damage is the result of bending about the weak axis (in the direction of the dead loads), then the flange vee heats will be working against the dead loads. Without the use of jacking forces to overcome the dead load moments, the straightening will be reduced or possibly be zero. If the damage was opposite to the direction of the dead load, the movement after heat straightening would be enhanced by the dead load.

**Figure 45. Dead load conditions on a simply supported beam.**

**Figure 46. PΔ effect on an axially loaded column.**

For columns and axially loaded members, the P-Δ effect must be considered. If an axially compressed member is damaged by lateral loads as shown in Figure 46, a moment is generated which is equal to P-Δ. This moment is in the opposite direction to the moment generated by a jacking force during the straightening process. If the lateral deflection is large, the moment due to the P-Δ effect could retard or prevent the restoration movement during heat straightening, or create instability when heating reduces steel strength.

##### 6.3.2 Response of Columns to Heat Straightening

With the axial load applied, a moment in the member is created due to the PD effect. This moment tends to impede the heat straightening process as it acts to magnify the damage. The approach recommended is to cancel out this moment with the application of the lateral jacking force. The jacking force should be adjusted to impose the specified jacking ratio plus inducing a moment to cancel out the PΔ moment at the center of damage. For each heating cycle the jacking force should be reduced to compensate for the reduced PΔ moment.To generalize, for a simply supported beam-column with the damage at an arbitrary location, the applied jacking force, P_{a}, is

(Eq. 6.11)

where P_{j} is the jacking force to create a specified moment at the damage location as a percentage of M_{p}, or

(Eq. 6.12)

and = column length, a and b = distances from end supports to the applied jacking load, and R = the jacking ratio, M_{j}/M_{p}. Pec is the additional jacking force required to cancel the eccentric moment due to the axial load, P, or

(Eq. 6.13)

Test results (Avent and Mukai, 1998) indicate that heat straightening can be successfully applied to axially loaded compression members. The results are plotted in Figure 47. Also shown is the theoretical curve for the beam without axial load based on the same parameters. The plastic rotations varied linearly with the jacking ratio, but they tended to be smaller than those predicted for the same beam without axial compression (Eq. 6.1). The axial force reduces the expected values compared to those without axial loads. Similar behavior was found for axially loaded compression members with Category S damage plastic rotations.

In summary, heat straightening is effective for axially loaded columns using the same patterns as for cases without axial compressive loads. The movements after heating will tend to be smaller than with zero axial loads on the same member. The jacking forces used should include, as a minimum, a component producing a moment at the damaged section equal and opposite to the moment produced by the axial compressive force acting through the deflection at the damaged section.

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