07-06-2010, 10:43 AM
I quote from a book called "Design of Reinforced Concrete Structures" -Chapter 6 by M.N.Hassoun:
"The moment of inertia, in addition to the modulus of elasticity, determines the stiffness of the flexural member. Under small loads, the produced maximum moment will be small and the tension stresses at the extreme tension fibers will be less than the modulus of rupture of concrete; in this case the gross transformed cracked section will be effective in providing rigidity. At working loads or higher, flexural tension cracks are formed...In both locations only the transformed cracked sections are effective in determining the stiffness of the member; therefore, the effective moment of inertia varies considerably along the span. At maximum bending moment, the concrete is cracked, and its portion in the tension zone is neglected in the calculations of the moment of inertia....Once cracks have developed, the assumption of uncracked section behavior under small loads does not hold."
I quote from a book called " Reinforced Concrete Structures" -Chapter 11 by R. Park, T.Paulay:
"Commonly, the flexural stiffness values used in the structural analysis are based on the gross concrete section; no allowance is made for concrete cracking and the steel is ignored...However, the change in the ratios of the flexural stiffnesses resulting from cracking may be significant in some cases...In fact, in may frames the beams will be cracked but the columns will remain uncracked in the service load range. the reduced flexural rigidity of cracked beams may lead to a bending moment to the columns larger than that calculated on the basis of gross section stiffnesses....To avoid significant moment redistribution, it may be better to base the moment of inertia of the beams on an approximate transformed cracked section (e.g. 0.5Ig) and the moment of inertia of columns on a the gross section Ig."
"The moment of inertia, in addition to the modulus of elasticity, determines the stiffness of the flexural member. Under small loads, the produced maximum moment will be small and the tension stresses at the extreme tension fibers will be less than the modulus of rupture of concrete; in this case the gross transformed cracked section will be effective in providing rigidity. At working loads or higher, flexural tension cracks are formed...In both locations only the transformed cracked sections are effective in determining the stiffness of the member; therefore, the effective moment of inertia varies considerably along the span. At maximum bending moment, the concrete is cracked, and its portion in the tension zone is neglected in the calculations of the moment of inertia....Once cracks have developed, the assumption of uncracked section behavior under small loads does not hold."
I quote from a book called " Reinforced Concrete Structures" -Chapter 11 by R. Park, T.Paulay:
"Commonly, the flexural stiffness values used in the structural analysis are based on the gross concrete section; no allowance is made for concrete cracking and the steel is ignored...However, the change in the ratios of the flexural stiffnesses resulting from cracking may be significant in some cases...In fact, in may frames the beams will be cracked but the columns will remain uncracked in the service load range. the reduced flexural rigidity of cracked beams may lead to a bending moment to the columns larger than that calculated on the basis of gross section stiffnesses....To avoid significant moment redistribution, it may be better to base the moment of inertia of the beams on an approximate transformed cracked section (e.g. 0.5Ig) and the moment of inertia of columns on a the gross section Ig."