Structural Design_2012_plastic_analysis firstx - PLASTIC ANALYSIS IN FRAMED STRUCTURES Dr-Ing Girma Zerayohannes Dr-Ing Adil Zekaria Dr-Ing Girma Z

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PLASTIC ANALYSIS IN FRAMED STRUCTURES Dr.-Ing. Girma Zerayohannes Dr.-Ing. Adil Zekaria Dr.-Ing. Girma Z. and Adil Z. 1
Chapter 5- Plastic Hinge Theory in Framed Structures 5.1 Introduction All codes for concrete, steel and steel-composite structures (EBCS-2, EBCS-3, EBCS-4) allow the plastic method of analysis for framed structures The requirement is that, sufficient rotation capacity is available at the plastic hinges Dr.-Ing. Girma Z. and Adil Z. 2
Chapter 5- Plastic Hinge Theory in Framed Structures In this chapter we will introduce the plastic method of analysis for line elements. It is called the “plastic hinge theory” The method is known as the “yield line theory” for 2D elements (e.g. slabs) Both are based on the upper bound theorem of the theory of plasticity Recall that the strip method is also a plastic method of analysis based on the lower bound theorem Dr.-Ing. Girma Z. and Adil Z. 3
Chapter 5- Plastic Hinge Theory in Framed Structures Therefore the capacity of the line elements are greater or at best equal to the actual capacity of the member. a concern for the designer, Dr.-Ing. Girma Z. and Adil Z. 4
Chapter 5- Plastic Hinge Theory in Framed Structures 5.2 Design Plastic Moment Resistances of Cross-Sections 5.2.1 RC Sections Such plastic section capacities are essential in the plastic hinge theory, because they exist at plastic hinges Dr.-Ing. Girma Z. and Adil Z. 5
Chapter 5- Plastic Hinge Theory in Framed Structures Determine using the Design Aid (EBCS-2: Part 2), the plastic moment resistance (the design moment resistance) of the RC section shown in following slide, if the concrete class and steel grade are C-25 and S-400 respectively. Dr.-Ing. Girma Z. and Adil Z. 6
Chapter 5- Plastic Hinge Theory in Framed Structures Dr.-Ing. Girma Z. and Adil Z. 7 Fig. Reinforced Concrete Section
Chapter 5- Plastic Hinge Theory in Framed Structures Steps: Assume that the reinforcement has yielded Determine C c c Determine M R,ds Check assumption of steel yielding Dr.-Ing. Girma Z. and Adil Z. 8
Chapter 5- Plastic Hinge Theory in Framed Structures Assume Reinforcement has yielded T s = A s f yd = 2 314 (400/1.15) = 218435 N from General design chart No.1 Sd.s = 0.195 Check the assumption that the reinforcement has yielded Dr.-Ing. Girma Z. and Adil Z. 9 22 . 0 350 250 33 . 11 218435 bd f C cd c c kNm bd f M cd s Sd s Sd 66 . 67 350 250 33 . 11 195 . 0 2 2 , , N bd f C T cd c c s 218435
Chapter 5- Plastic Hinge Theory in Framed Structures yd = f yd /E s = 347.8/200000 = 1.739( 0 / 00 ) s = 9.4( 0 / 00 ) 1.739( 0 / 00 ) reinforcement has yielded Exercise for section with compression reinforcement Dr.-Ing. Girma Z. and Adil Z. 10
Chapter 5- Plastic Hinge Theory in Framed Structures Dr.-Ing. Girma Z. and Adil Z. 11
Chapter 5- Plastic Hinge Theory in Framed Structures 5.2.2 Structural Steel Sections Consider the solid rectangular section shown in the next slide The plastic section capacity, M pl is: M pl = y ( bd 2 /4 ); ( bd 2 / 4 ) is called the plastic section modulus and designated as W pl The elastic section modulus W el = bd 2 /6 Dr.-Ing. Girma Z. and Adil Z. 12