Moment-Curvature Analysis

Moment-Curvature Analysis

1. 1. Analysis Assumptions and General Procedure

   • 1. Sections that are before loading remain plane after loading.
   • 2. The stress-strain relations are know from properties measures in coupon tests on concrete and reinforcing steel.
   • 3. Equations of equilibrium can be used to calculate the axial force and moment on the cross section given the internal stresses.
   • Strain varies across the section

2. 2. Linear-Elastic Response of Uncracked Sections

   • The croncrete and compression steel are responding in the linear-elastic range.
   • Where the greater accuracy is desired, or for higher computed compressive stresses, procedures accounting for nonlinearity of the concrete stress-strain relation can be used.
   • Understimate stiffness under service loads becuause of tension-stiffening of th textural tension zone.

3. 3.Flexural Stiffness at Services Loads

   • The gross section moment of inertia provides an adequate measure of flexural stiffness for members that are not cracked by services loads.
   • The degree of the understimation depends on the longitudinal reinforcement ratio and service load intensity relative to the cracking load.
   • Branson
   • Brischoff
     • Relative stiffness according to Eqs.

4. 4.Response at Ultimate Limit States

   • Cover concrete spalling can be the ultimate limit state for unconfined sections under gravity loads.
   • Reinforcement fracture can be the ultimate limit state for a confined section under earthquake loading.
   • The usual approach is to asumme that cover concrete behaves unconfined concrete for strains less than Esp and that it resists no stress for larger strain,

5. 5. Compression Stress Block Parameters

   • To calculate internal forces on a cross section, it is useful to determine the magnitudes and centroidal locations of the internal stress resultants.
   • We must evaluate compressive blocks or a more general formulation.
     • General approach for a rectangular compression zone.
     • Various building codes have adopted the equivalent rectangular stress block approach for calculating strength of members subjected to moment with or without axial load, but with different parameters for α1 y β1.
     • Test result high-strength concrete have led to proposal for additional modifications to the stress block parameters.

6. 6.Automation of Moment-Curvature Calculations

   • The calculations can be programmed to be solved by computer software.
     • A widely used approach in which the cross section is subdivided into fibers.
       • The stress is defined based in the assigned material and the centroidal strain, and a fiber stress resultant acting at the fiber centroid is then defined by the product of the stress and fiber area.

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