chap2 - CE 405: Design of Steel Structures Prof. Dr. A....

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Unformatted text preview: CE 405: Design of Steel Structures Prof. Dr. A. Varma Chapter 2. Design of Beams Flexure and Shear 2.1 Section force-deformation response & Plastic Moment (M p ) A beam is a structural member that is subjected primarily to transverse loads and negligible axial loads. The transverse loads cause internal shear forces and bending moments in the beams as shown in Figure 1 below. w P V(x) M(x) x w P V(x) M(x) x Figure 1. Internal shear force and bending moment diagrams for transversely loaded beams. These internal shear forces and bending moments cause longitudinal axial stresses and shear stresses in the cross-section as shown in the Figure 2 below. V(x) M(x) y d b dF = b dy V(x) M(x) y d b dF = b dy Curvature = = 2 /d = +- 2 / d 2 / d dy b F y dy b M 2 / d 2 / d = +- (Planes remain plane) Figure 2. Longitudinal axial stresses caused by internal bending moment. 1 CE 405: Design of Steel Structures Prof. Dr. A. Varma Steel material follows a typical stress-strain behavior as shown in Figure 3 below. y y u u y y u u Figure 3. Typical steel stress-strain behavior. If the steel stress-strain curve is approximated as a bilinear elasto-plastic curve with yield stress equal to y , then the section Moment - Curvature (M- ) response for monotonically increasing moment is given by Figure 4. M y M p A: Extreme fiber reaches y B: Extreme fiber reaches 2 y C: Extreme fiber reaches 5 y D: Extreme fiber reaches 10 y E: Extreme fiber reaches infinite strain A B C E D Curvature, Section Moment, M y y y y y y y y y y y y 2 y 2 y 5 y 5 y 10 y 10 y A B C D E M y M p A: Extreme fiber reaches y B: Extreme fiber reaches 2 y C: Extreme fiber reaches 5 y D: Extreme fiber reaches 10 y E: Extreme fiber reaches infinite strain A B C E D Curvature, Section Moment, M y y y y y y y y y y y y 2 y 2 y 5 y 5 y 10 y 10 y A B C D E y y y y y y y y y y y y y y y y y y y y y y y y 2 y 2 y 2 y 2 y 5 y 5 y 5 y 5 y 10 y 10 y 10 y 10 y A B C D E Figure 4. Section Moment - Curvature (M- ) behavior. 2 CE 405: Design of Steel Structures Prof. Dr. A. Varma In Figure 4, M y is the moment corresponding to first yield and M p is the plastic moment capacity of the cross-section. The ratio of M p to M y is called as the shape factor f for the section. For a rectangular section, f is equal to 1.5. For a wide-flange section, f is equal to 1.1....
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chap2 - CE 405: Design of Steel Structures Prof. Dr. A....

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