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Plastic Analysis-HW - Plastic Analysis and Design of Beams...

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Plastic Analysis and Design of Beams The current AISC specifications for structural steel buildings, both ASD and LRFD, allow the plastic design of braced frame members (including beams) meeting the compact section criteria. The mill specified yield stress, F y , shall not exceed 65 ksi. However, the current AASHTO specifications, both ASD and LRFD, do not allow the plastic design of highway bridge structures. Article 48.1.3 (Part D, Load Factor Design) of AASHTO Standard Specifications for Highway Bridges, 17th ed., allows redistribution of the negative moments (partial recognition of plastic behavior in redundant beams) caused by the gravity load in some flexural members meeting the requirements of compact section criteria. In the classical elastic design method, the maximum load a member could support was assumed to be equal to the load that would cause the most highly stressed fiber (a single point in a structure) to reach F y . However, statically indeterminate structures made of a ductile material (steel) have the capability to redistribute internal force distributions by local yielding upon being overloaded before reaching a collapse mechanism. Consider a propped beam of length L subjected to a concentrated load P at the mid-span. y F y F y F / 2 l y f F < p y M F Z = p y Z S M M y y M F S = 1 5 32 P l 1 3 16 P - l 1 P : natural hinge •: plastic hinge o Collapse mechanism 2 4 P l 2 P 1 2 S: elastic section modulus Z: plastic section modulus P 1 3 16 p P M = l 1 2 u P P P = + 1 2 1 1 2 5 3 32 4 16 8 P P P P P + = = l l l 3 1 1 7 768 P EI ∆ = l 3 2 2 48 P EI = l service load 1 9 8 u P P = 1 0.66 1.7 u s P P P = = 1 / 2 l u P
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Plastic Design h Ease of structural analyses as the prerequisite of the design. h Results in a consistent margin of safety for all structures, independent of the degrees of static indeterminacy. h Results in a considerable cost savings for bending type indeterminate structures. h Of determinate beams yields the same design as by ASD. h Of tension and compression members yields no better design. h Is not suitable for situations where fatigue stresses are a problem. h Must have a ductile material to employee plastic design. h Requires compact section criteria along with excessive bracing of compression flanges.
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