# Write a formula for moment of resistance of composite beam

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The consequences are that: Flanges can be equal or unequal Hybrid sections comprising plates of different strengths are possible Girders can be straight or curved in plan Girders can be straight or curved in elevation to suit the road profile Girders can be of variable depth, with straight or curved soffits Girders can be of uniform or variable section along their length e.

Additionally, web thicknesses are often thin relative to their depth and then the local buckling of the web may need to be taken into account which is not usually the case for rolled sections.

The bending resistance of the cross section should be verified at every cross section.

The Eurocode rules give the value of design resistance moments for a beam related to its cross-section. The buckling resistance of the member over a discrete length between restraints must also be verified.

Typically, the buckling resistance of the member will govern, rather than the resistance of the most highly stressed cross section.

Cross section resistance and buckling resistance are discussed separately below, both for bare steel beams and for composite beams. Such local buckling is fundamental to the behaviour and therefore to the design of all structural components carrying compressive stress.

This compression arises from either compression force or bending moment. Classification of a steel section is therefore one of the first tasks to be undertaken in design.

There are four classes of cross section: Class 1 — The section can form a plastic hinge and has sufficient rotational capacity to maintain this moment over a considerable range of in-plane rotation Class 2 — The section can develop plastic resistance but has limited rotational capacity to act as a hinge Class 3 — The section can develop elastic resistance of the full cross-section Class 4 — Local buckling of slender elements reduces the elastic resistance; the section can develop elastic resistance of an effective cross-section, smaller than the full section.

In bridges, plastic global analysis is rarely used, so Class 1 offers no benefit over Class 2. The classification of a cross section depends on the width to thickness ratio of the parts of the section subject to compression. This includes all parts of the cross section either totally or partially in compression under the action combination considered.

In general, it is possible for flanges and webs to be in different classes and a cross section is usually classified by the highest least favourable class of its component parts.

However, it is also permitted to define a section by quoting both the flange classification and web classification separately. The tables are generic and account for cases of pure compression, pure bending or a combination of bending and compression for internal compression parts, outstand flanges, angles and tubular sections.

Different approaches to cross-section bending resistance design are required depending on the class of the section. For Class 1 and 2 sectionsthe design resistance of the cross section corresponds to a fully plastic internal stress distribution as shown below.

The resistance moment is therefore given by However, it should be noted that the plastic section modulus Wpl can only be derived solely from the geometry if the yield strength is the same for all parts of the cross section. Where yield strength varies thicker elements generally have a lower yield strength the resistance moment should be determined directly from the plastic stress blocks.

Stress block for Class 1 and 2 sections Class 3 cross-sections can develop compressive yield at their extreme fibres defined in EN [1] as being at the mid-plane of a flange rather than its outer surface but will fail by local buckling if this yielding starts to spread further into the cross section.

The maximum resistance is therefore reached when the extreme compression fibre reaches yield. If partial plastification of the tension zone is not considered in design, the resistance will be reached when the stress from an elastic stress distribution reaches yield at either fibre, whether compressive or tensile, as shown below.

Elastic stress distribution for Class 3 sections The resistance moment is then given by: If the limiting fibre is on the tensile side, partial plastification of the tension zone of the web may be considered, although this is often ignored.

The development of partial plastification is shown below. Partially plastic stress distribution for Class 3 sections The resistance moment is then determined by assuming plane sections remain plane, a bilinear stress-strain curve and by balancing forces in the tension and compression zones.

Note that the neutral axis will move as plasticity spreads throughout the tension zone and this can then affect the section classification, hence why partial plastification is usually ignored.

Class 4 sections fail by local buckling before they reach yield. Two approaches are given in EN [2] to determine the bending resistance of such sections: Limiting stress method Effective area method For the limiting stress method, the gross cross-section is used. The resistance moment is deemed to be obtained when the weakest panel in compression fails by local buckling.

This method can often be conservative as it does not allow for the shedding of load between panels. The more usual approach is to use the effective area method, where the resistance moment is obtained when yield is reached at an extreme fibre of the effective cross-section as shown below for the more general case of a box sectionwhen both the flange and the web might be class 4.Write the transfer equation.

Ixa = _____ Correct response to preceding frame Now you have all the necessary tools for finding moments of inertia of composite areas. All that remains is to learn to use them on composite areas.

find in a later course that the strength of a beam is directly related to the moment of inertia of its cross. This is because the composite beam is one piece, so the full depth of the beam (h) goes into the second moment of area; Weight saving will be significant. Whiteboard. Some wisdom: Look, there are many good knife steels out there.

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