Steel is a high-strength 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.
D-1. 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 all-purpose carbon-grade steel. It is widely used in building and bridge construction.
HIGH-STRENGTH, LOW-ALLOY STEEL
D-2. High-strength steels may be used where lighter, stronger members are required. High-strength steels are necessary as a member becomes smaller because of instability, local buckling, deflection, and other similar failures. High-strength 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 atmospheric-corrosion-resistant 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 TEMPERED-ALLOY STEEL
D-3. ASTM A514 steel is an example of this type of steel. It provides yield strengths in excess of 90 ksi. As with all high-strength steels, cost is a crucial factor in deciding whether to use them.
D-4. 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 weakest-strength steel for classification and design purposes.
D-5. Table D-1 lists the standard steel-plate thicknesses, and Tables D-2 through D-10 list the section properties for the most common structural shapes available in the US. I-beams come in two different shapes-wide-flange (W-shaped) and American-standard (S-shaped). W-shaped beams have essentially parallel flange surfaces and are the most common shape used in bridge construction. W-shaped beams are most economical when moment controls the design of a span. S-shaped beams have flanges that are sloped toward the edges and have a larger web area than W-shaped beams. S-shaped beams are more economical when shear controls the design of a span. Steel channels (C-shaped beams) have the same characteristics as the S-shaped beams and are usually used for lateral bracing and as truss-chord components. Equal-leg and unequal-leg angles (L-shaped beams) are also used as lightweight bracing materials. Bearing piles (HP-shaped beams) are used in substructures to provide support for the bridge.
UNLISTED-BEAMS SECTION PROPERTIES
D-6. Tables D-2 , D-3 , D-4 , D-6 , and D-7 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
D-7. Compute the effective shear area as follows:
D-8. 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 D-1 ).
Symmetrical, complex shapes. Divide the depth of the member by two ( Figure D-2 ).
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 D-3 ).
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 D-4 ).
Determine the area of each of the simple shapes ( Figure D-5 ).
Determine the distance from the baseline to the neutral axis of the complex shape by using Figure D-6 and the following equation:
Figure D-1. Neutral Axis in Simple Shapes
Figure D-2. Neutral Axis in Symmetrical, Complex Shapes
Figure D-3. Sectioning Complex Shapes
Figure D-4. Determining Baseline-to-Neutral-Axis Distances
Figure D-5. Areas of the Simple Shapes
Figure D-6. Example Tabulation of Neutral Axis
MOMENT OF INERTIA
D-9. Compute the moment of inertia of a shape (with respect to the axis) using Figure D-6 and the following equation:
D-10. 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 D-7 ). Compute as follows:
Simple shapes ( Figure D-8 ).
Complex shapes. Use the parallel-axis theorem, which dictates the use of Figure D-9 and the following equation:
Figure D-7. Axis Orientations Based on Loading
Figure D-8. Moments of Inertia for Simple Shapes
Figure D-9. Sample Tabulation of Moments of Inertia
D-11. 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
D-12. Use Figure D-10 and the following equation (based on the parallel-axis theorem) to approximate the section modulus for symmetrical, built-up beams and girders that have been welded within 5 percent of the true section modulus:
Figure D-10. Built-up Beams
Symmetrical, Riveted Beams and Girders
D-13. Use the following equation and Figure D-11 to approximate the section modulus of these beams and girders (deduct the area of the rivet holes from the used areas):
Figure D-11. Riveted Beam or Girder
All Shapes (Symmetrical and Unsymmetrical)
D-14. 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
D-15. 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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