Chapter 9 Two-way slabs and yield-line analysis
Chapter 9 Two-way slabs and yield-line analysis
One-way slabs and two-way slabs ·One-way slabs which as the name implies span in one direction is principle analyzed and designed as beams and present no special problems ·Two-way slabs The design of two-way slabs presents varying degrees of difficulty depending on the boundary conditions For irregular cases,the yield-line theory provides a powerful design tool as we shall see in the following sections of this chapter
One-way slabs and two-way slabs • One-way slabs which as the name implies span in one direction is principle analyzed and designed as beams and present no special problems • Two-way slabs The design of two-way slabs presents varying degrees of difficulty depending on the boundary conditions For irregular cases, the yield-line theory provides a powerful design tool as we shall see in the following sections of this chapter
Yield-line analysis o Ultimate-load theory The yield-line theory pioneered by Johansen is an ultimate-load theory for slab design and is based on assumed collapse mechanisms and plastic properties of under-reinforced slabs ·Yield line The assumed collapse mechanism is defined by a pattern of yield line,along which the reinforcement has yielded and the location of which depends on the loading and boundary conditions
Yield-line analysis • Ultimate-load theory The yield-line theory pioneered by Johansen is an ultimate-load theory for slab design and is based on assumed collapse mechanisms and plastic properties of under-reinforced slabs • Yield line The assumed collapse mechanism is defined by a pattern of yield line, along which the reinforcement has yielded and the location of which depends on the loading and boundary conditions
Restriction of Yield-line analysis 1.For the yield-line theory to be valid,shear failures, bond failures.and primary compression failures in flexure must all be prevented; 2.The moment/curvature relationship must have a long horizontal portion when the yield capacity of the slab is reached: In practice,this restriction presents no difficulties because slabs are usually very much under-reinforced
Restriction of Yield-line analysis 1、For the yield-line theory to be valid, shear failures, bond failures. and primary compression failures in flexure must all be prevented; 2、The moment/curvature relationship must have a long horizontal portion when the yield capacity of the slab is reached; In practice, this restriction presents no dif iculties because slabs are usually very much under-reinforced
Typical yield-line patterns Simple supports Yield lines support Fre edge Simple Yield line SImple support (a) (b) Negative yield line Simple support a6pa paxid 77777777777 Simple support Yield ifne in different slab patterns
Typical yield-line patterns Yield line in different slab patterns