Mechanics of Materials-Steel

Transcription

1 Mechanics of Materials-Steel Structural Steel Structural steel considered one of the predominant materials for construction of buildings, bridges, towers and other structures. The preferable physical properties of steel makes it widely used for construction of steel bridges, high rise buildings, and other structures. The high strength, ductility, toughness, and uniformity are some of the desirable properties that made steel a leading martial for structures. Despite steel desirable properties, disadvantages of using steel include associated maintenance cost, fatigue, and susceptibility to buckling Stress-Strain Relationship The stress-strain relationship of steel material as plotted by the results of a tensile test is shown in Figure 1. The relationship is linear up to the proportional limit; where the material follows the Hook s law. The upper yield point in the curve is the peak value reached after the linear part; the peak value is followed by a lower yield point at which the curve levels off. Elastic limit Upper yield point A Proportional limit Lower yield point 0 B ε Elastic Plastic Strain Hardening Necking and failure 1

2 As shown in the curve, the stress remains constant while the strain continues to increase. At that stage the elongation continues as long as the load is not removed. The constant stress region of the curve called the yield plateau, or plastic range. The strain hardening of the stress-strain curve begins at a strain of approximately 12 times the strain at yield. At that stage, additional stress is required to further extend the material until a maximum stress is reached, after which the stress decreases with increasing the strain, and then fracture occurs. This behavior as exhibited by the curve is called ductility, which allows the steel material to largely deform before fracturing. The elastic limit of the material is the stress on the curve that lies between the proportional limit and the upper yield point. If the material is loaded to a stress lower than this value, unloading will not induce any permanent deformations. Unloading before elastic limit will follow the linear path developed during loading the material. Unloading from a point beyond the elastic limit will follow a path parallel to the linear part but it would produce a permanent deformation. Idealized Stress-Strain Relationship In idealized stress strain curve as shown in Figure 2, the proportional limit, elastic limit, and the upper and the lower yield point are represented by a single point called yield point, defined by the stress F y. The maximum stress in the idealized curve represents the ultimate tensile strength F u. It should be noted that the shape of the curve below is typical for mild structural steels which are different from each other in the values of F y and F u. The ratio of the stress to strain within the elastic range called Young's modulus and denoted by E. The modulus of elasticity, E, is the same for all structures steel and has a value of 29,000,000 psi. 2

3 F u F y 1 E Figure 2 High Strength Steel High strength steel is less ductile than mild structural steel discussed above. A typical stress-strain curve is shown in Figure 3. It can be noted that there is no well-defined yield point or yield plateau in the curve. To define the yield strength, a stress at the point of unloading that corresponds to a strain of is used. This method of determining the yield strength is called the 0.2% offset method. The two properties usually needed for steel design are F u and F y regardless of the shape of the stress-strain curve and regardless of how F y was obtained. ε 3

4 F u F y Tensile strength Yield strength Elastic limit 1 E Residual strain Figure 3 ε Properties of Steel The properties of structural steel are determined by the quantity of carbon and other elements that are present in the chemical composition. Elements such as Silicon; Nickel; Manganese; and Copper are normally added. Steel having significant amount of these elements is referred to as an alloy steel. Structural steels can be categorized according to their chemical composition into plain carbon steels, low-alloy steels, and high-alloy steels. Grades of Structural Steel Structural steels are generally grouped into several ASTM classifications which are identified by the designation assigned by the ASTM. Grade A36 steel with F y =36 ksi and F u = 58 ksi is one of the most commonly mild structural steel used. Other grades used are A572 Grade 50 and A992. More information is available for each grade of steel in the AISC Steel Construction Manual. The steel grades for the available structural shapes are shown in Table 2-3 of the AISC Steel Construction Manual. 4

5 Structural Shapes One of the objectives of the design is to select the adequate section for the individual member under consideration. Most frequently, the selection involves choosing a standard section from the shapes that are available. Most of the standard shapes are produced by hot-rolling manufacturing process. Symbols for the structural shapes of some of the widely used hot-rolled shapes are shown in Table 1. 5

6 The dimensions and designations of the standard available shapes can be found in the AISC Steel Construction Manual. Usually, the shapes with large moments of inertia compared to their areas are preferable. The commonly used I, T, and C shapes fall into this category. As shown in the AISC Steel Construction Manual, the steel cross-sections are designated by their shapes, for example there are angles, tees, and plates. One important distinction with regard to defining the shapes, is the American standard beams (S beams) and the wide-flange beams (W beams) as they are both I-shaped as shown in Figure 4. The wide-flange shape is designated by the nominal depth and the weight per foot, such as a W16X100 which has a nominal 16 in depth and weighs 100 pounds per foot. 6

7 W-shape Beam Standard Beam Figure 4 7

8 Example Problem (1) A structural shape of A588 Steel is to be used as a beam in a building structure. What are the values of the yield stress F y, ultimate tensile strength Fu, and the modulus of elasticity E. a. F y = 36 ksi, F u = 58 ksi, E = 29,000 ksi b. F y = 50 ksi, F u = 58 ksi, E = 29,000 ksi c. F y = 50 ksi, F u = 70 ksi, E = 29,000 ksi d. F y = 65 ksi, F u = 80 ksi, E = 29,000 ksi Referring to Table 2-3 of the AISC Steel Construction Manual, F y = 50 ksi, F u = 70 ksi, and E = 29,000 ksi for all grades of types of steel. Answer: c Example Problem (2) A W18X97 is to be used as a beam in a building structure. What is the selfweight of the beam if a span of 50 ft is required? a kips b kips c kips d kips A W18X97 weight 97 Ib/ft, so for a beam of 20 ft span: Weight of beam = (97 Ib/ft)(50ft)=4,850 Ib = 4.85 kips Answer c. 8