Limit of Proportionality

In a solid beam, the compressive and tensile stresses are not confined to the surfaces. The compressive stress in a section is highest at the upper surface and gradually diminishes to zero at the neutral plane. Similarly, the tensile stress is highest on the lower surface and diminishes to zero at the neutral plane (Figure 10.6a). While the beam deforms elastically, the compressive and tensile stresses increase proportionately with distance from the neutral plane. The compressive stress at a distance, d, above the neutral plane will be the same as the tensile stress at a distance, d, below the neutral plane. Further, as the modulus of elasticity is the same in compression and tension, the strain at both positions will be similar. Simple beam theory assumes that the beam behaves elastically until failure. However, the limit of proportionality in compression is quite low and once exceeded the fibres near the upper surface will start to buckle, crash, and strain at a greater rate while... 

Pelzer also succeeded in working out a theoretical extension curve which agrees fairly with the experiments, even outside the limit of proportionality between stress and elongation. This extension curve is represented by... 

A = Elongation, = Module of elasticity, Rp = Limit of proportionality, HV = Vickers hardness, Rm = Tensile strength... 

EN 14651 2005 Test Method for Metallic Fibre Concrete - Measuring the flexural tensile strength (limit of proportionality (LOP), residual). 

Main test results are presented in Table 3. Layout of the table corresponds to that of the Table 2. Each experimental value is an average of test results of 4 specimens. More detailed results can be found in [5]. In the Table 3 presented are for each series of specimens observed maximum bending stress (f or MOR), limit of proportionality [Pg.623]

From this curve, the limit of proportionality, is calculated as... 

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