Appendix D
Steel Properties
Steel is a highstrength material made of a combination of iron (with a small percentage [usually less than 1 percent] of carbon) and trace percentages of some other elements. Steel has been made for thousands of years, but an economical process for mass production was not developed until the 1800s. Steel's high strength and relatively low weight makes it extremely desirable as a construction material.
ALLPURPOSE STEEL
D1. Different grades of steel are available for constructing bridges and buildings. Each has advantages and disadvantages when compared to the type of construction desired. A36 steel is an allpurpose carbongrade steel. It is widely used in building and bridge construction.
HIGHSTRENGTH, LOWALLOY STEEL
D2. Highstrength steels may be used where lighter, stronger members are required. Highstrength steels are necessary as a member becomes smaller because of instability, local buckling, deflection, and other similar failures. Highstrength steel is frequently used in tension members, in beams of continuous and composite construction where deflection is minimized, and in columns having low slenderness ratios. The following steels are in this category:
 ASTM A529 structural carbon steel. These steels have a yield strength of 42 ksi. Their other properties are similar to A36 steel.
 ASTM A441 and A572 structural steels. These steels provide yield strengths from 40 to 65 ksi. Some types may be more brittle than A36 steel.
 ASTM A242 and A588 atmosphericcorrosionresistant steels. These steels are suitable for use in a bare (unpainted) condition. Exposure to normal atmospheric conditions cause a tightly adherent oxide (rust) to form on the surface that protects the steel from further, more destructive oxidation. The reduction of maintenance expense for these steels may offset their higher initial cost during peacetime construction.
QUENCH AND TEMPEREDALLOY STEEL
D3. ASTM A514 steel is an example of this type of steel. It provides yield strengths in excess of 90 ksi. As with all highstrength steels, cost is a crucial factor in deciding whether to use them.
STEEL STRENGTHS
D4. If the type of steel is unknown, use A36 specifications with a minimum yield strength of 36 ksi. If in doubt about the strength of the steel, always use the weakeststrength steel for classification and design purposes.
STRUCTURAL SHAPES
D5. Table D1 lists the standard steelplate thicknesses, and Tables D2 through D10 list the section properties for the most common structural shapes available in the US. Ibeams come in two different shapeswideflange (Wshaped) and Americanstandard (Sshaped). Wshaped beams have essentially parallel flange surfaces and are the most common shape used in bridge construction. Wshaped beams are most economical when moment controls the design of a span. Sshaped beams have flanges that are sloped toward the edges and have a larger web area than Wshaped beams. Sshaped beams are more economical when shear controls the design of a span. Steel channels (Cshaped beams) have the same characteristics as the Sshaped beams and are usually used for lateral bracing and as trusschord components. Equalleg and unequalleg angles (Lshaped beams) are also used as lightweight bracing materials. Bearing piles (HPshaped beams) are used in substructures to provide support for the bridge.
UNLISTEDBEAMS SECTION PROPERTIES
D6. Tables D2 , D3 , D4 , D6 , and D7 do not list the section properties for all beam types. These properties can be determined by using the external dimensions of the unlisted beams and calculating each of the section properties. Important properties to consider include the
 Effective shear area.
 Neutral axis.
 Moment of inertia.
 Section modulus.
 Radius of gyration.
EFFECTIVE SHEAR AREA
D7. Compute the effective shear area as follows:


NEUTRAL AXIS
D8. The neutral axis is the plane that splits the area of a shape in half. The beam is unaffected by compression or tension along this axis. There is no stress in the beam along this axis. Determine the location of the neutral axis as follows:
 Simple shapes (squares, rectangles, triangles, and circles). Divide the depth of the shape by two or three, as appropriate ( Figure D1 ).
 Symmetrical, complex shapes. Divide the depth of the member by two ( Figure D2 ).

Unsymmetrical, complex shapes. Use the following procedure:
 Divide the complex shape into simple shapes and determine the location of the neutral axes in these sections ( Figure D3 ).
 Find the distance from an arbitrary baseline (normally the bottom of the complex shape) to the neutral axis of each of the simple shapes ( Figure D4 ).
 Determine the area of each of the simple shapes ( Figure D5 ).

Determine the distance from the baseline to the neutral axis of the complex shape by using Figure D6 and the following equation:
Figure D1. Neutral Axis in Simple Shapes
Figure D2. Neutral Axis in Symmetrical, Complex Shapes
Figure D3. Sectioning Complex Shapes
Figure D4. Determining BaselinetoNeutralAxis Distances
Figure D5. Areas of the Simple Shapes
Figure D6. Example Tabulation of Neutral Axis
MOMENT OF INERTIA
D9. Compute the moment of inertia of a shape (with respect to the axis) using Figure D6 and the following equation:


D10. The moment of inertia of a given shape changes with the differing locations and orientations of the axis chosen. The axis normally chosen is the neutral axis of the cross section of the beam that is perpendicular to the load being applied ( Figure D7 ). Compute as follows:
 Simple shapes ( Figure D8 ).

Complex shapes. Use the parallelaxis theorem, which dictates the use of Figure D9 and the following equation:
Figure D7. Axis Orientations Based on Loading
Figure D8. Moments of Inertia for Simple Shapes
Figure D9. Sample Tabulation of Moments of Inertia
SECTION MODULUS
D11. Compute the stress induced in the extreme fiber of a given shape as follows. The value of Mi/ye is defined as the section modulus of the shape. It is a measure of the ability of the shape to resist bending moments about a given axis.


Symmetrical, Welded Beams and Girders
D12. Use Figure D10 and the following equation (based on the parallelaxis theorem) to approximate the section modulus for symmetrical, builtup beams and girders that have been welded within 5 percent of the true section modulus:


Figure D10. Builtup Beams
Symmetrical, Riveted Beams and Girders
D13. Use the following equation and Figure D11 to approximate the section modulus of these beams and girders (deduct the area of the rivet holes from the used areas):


Figure D11. Riveted Beam or Girder
All Shapes (Symmetrical and Unsymmetrical)
D14. Compute the section modulus of all types of shapes as follows:
 Determine the location of the neutral axis as described earlier.
 Determine the moment of inertia of the shape about the neutral axis as described earlier.
 Determine the distance from the neutral axis to the point on the section that is the farthest away from the neutral axis.
 Divide the moment of inertia by the neutral axis.
RADIUS OF GYRATION
D15. The radius of gyration for a shape is the distance from a given axis (usually the neutral axis) where the concentrated mass of the shape would have the same moment of inertia as the actual shape. This value is a measure of how the shape reacts to rotational forces. The purpose of computing the radius of gyration is to determine the capacity of the shape to resist buckling that is induced from compressive and bending forces. Compute the radius of gyration as follows:


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