Outline_11

Outline_11 - 1.054/1.541 Mechanics and Design of Concrete Structures Prof Oral Buyukozturk Spring 2004 Massachusetts Institute of Technology

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk 1 / 9 Massachusetts Institute of Technology 1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 11 Yield Line Theory for Slabs ± Loads and load effects z x h x Vdy y Vdx dy y y V Vd y y ⎛⎞ + ⎜⎟ ⎝⎠ d x qdxdy x x V x x + d y dx y Surface and shear forces y mdx yx md x yx yx m y y + d x y y m y y + d x x x m x x + d y xy xy m x x + d y y Ndx y xy Nd y x Ndy yx x x x N x x + d y xy xy N x d y x + yx yx N y y + d x y y N y d x y + x xy y x mdy dy dx y x Membrane forces Moments
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 11 o Load effects to be solved: ,, , , , , , , , x y x y xy yx x y xy yx VVmmm m N N N N Æ Ten unknowns and six equations Æ Indeterminate problem: We need to include stress-strain relation for complete elastic solution. o The relative importance of the load effects is related to the thickness of the slab. Most reinforced and prestressed concrete floor slabs fall within “medium-thick” class, i.e., plates are ± thin enough that shear deformations are small, and ± thick enough that in-plane or membrane forces are small. ² Analysis methods: o Elastic theory o Elastic-plastic analysis – Finite element analysis (FEA) o Approximate methods of analysis o Limit analysis – Yield Line Theory – Lower & upper bound analysis ² Elastic theory o Lagrange’s fourth-order PDE governing equation of isotropic plates loaded normal to their plane: 44 4 42 2 4 2 www q x xy y D ∂∂ ++ = where w = deflection of plate in direction of loading at point ( , x y ). q = loading imposed on plate per unit area, () , qfx y = flexural rigidity of plate, D 3 2 12(1 ) Eh D µ = E = Young’s modulus h = plate thickness 2 / 9
Background image of page 2
1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 11 µ = Poisson’s ratio. o Navier’s solution of Lagrange’s equation using doubly infinite Fourier series: () 11 ,s i n mn mn mx ny wxy qC A ab s i n π ∞∞ == =⋅⋅ ∑∑ where = lengths of panel sides , = integers , = constants – Boundary conditions. , mn CA ± Finite difference (FD) method o
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/29/2011 for the course CIVIL 1.018j taught by Professor Markusbuehler during the Fall '08 term at MIT.

Page1 / 9

Outline_11 - 1.054/1.541 Mechanics and Design of Concrete Structures Prof Oral Buyukozturk Spring 2004 Massachusetts Institute of Technology

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online