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Moment of Inertia of Area
Published in M. Rashad Islam, Md Abdullah Al Faruque, Bahar Zoghi, Sylvester A. Kalevela, Engineering Statics, 2020
M. Rashad Islam, Md Abdullah Al Faruque, Bahar Zoghi, Sylvester A. Kalevela
In civil engineering, the moment of inertia of a beam is a very important property used in the calculation of the beam’s deflection caused by a moment applied to the beam. The moment of inertia is an indication of the stiffness of a beam, which is the resistance to deflection of the beam when carrying loads that tend to cause it to bend. It provides the beam’s resistance to bending due to an applied moment, force, or distributed load perpendicular to its neutral axis, as a function of its shape. The polar second moment of area provides insight into a beam’s resistance to torsional deflection, due to an applied moment parallel to its cross-section, as a function of its shape. In summary, moment of inertia is a geometric property of a section which controls the deflection (Figure 10.1) and the stress-carrying capacity of a section. The larger the moment of inertia, the lower the possible deflection and stress level in the beam. It also helps a column to resist buckling.
Simply supported beams
Published in Mike Tooley, Lloyd Dingle, Engineering Science, 2020
The second moment of area I is a measure of the bending efficiency of the structure, in that it measures the resistance to bending loads. The greater the distance and amount of mass of the structure away from the bending axis, the greater the resistance to bending.
Properties of sections
Published in Surinder S. Virdi, Advanced Construction Mathematics, 2019
The second moment of area is a property of an area used in several civil engineering and structural engineering calculations. It is denoted by I, and is used in the theory of bending which states that MI=σy=ER
TAMU-POST: An analysis tool for vehicle impact on in-line pile group
Published in Cogent Engineering, 2020
Asadollahi Pajouh Mojdeh, Briaud Jean-Louis
where Eb is the elastic modulus of the beam, Ib is the second moment of area (moment of inertia) of the beam with respect to the axis perpendicular to the applied load, y, and x are the beam deflection and the distance along the beam, respectively, q(x, t) is the transverse load applied at a distance x and at a time t. The load itself was not constant and varied with time; therefore, the equation controlling the behavior of the SDOF mass-spring-dashpot model with an applied load varying with the time t was:
How to build vegetation patches in hydraulic studies: a hydrodynamic-ecological perspective on a biological object
Published in Journal of Ecohydraulics, 2023
Loreta Cornacchia, Garance Lapetoule, Sofia Licci, Hugo Basquin, Sara Puijalon
Biomechanical traits were measured through bending tests on 10 replicate individuals per species using a universal testing machine (Instron 5942, Canton, MA, USA). The species considered all have a caulescent growth form: the stem bears the leaves (canopy), and the bending of the stem is a key element for plant bending (movement with the flow) and canopy reconfiguration. Therefore, bending tests were carried out on the basal part of the main stem (Hamann and Puijalon 2013). However, due to the very high flexibility of the stems of the species studied, a three-point bending test could not be performed on the samples because the samples tend to slip off the support bars. The samples were tested as cantilever beams using a one-fixed end bending test (Hamann and Puijalon 2013), where each stem sample (5 cm in length) was clamped horizontally at its basal end while a force was applied at the midpoint of the sample by lowering a probe at a constant rate of 10 mm min−1. The following biomechanical traits were calculated: The bending Young’s modulus (E in MPa) quantifies the sample stiffness and is defined as the slope of a sample’s stress–strain curve in the elastic deformation region.The second moment of area (I in m4) quantifies the distribution of material around the axis of bending, accounting for the effect of the cross-sectional geometry of a structure on its bending stress. Because the stem cross-sections for C. platycarpa, G. densa and Elodea sp. are approximately circular, I was calculated as I = (πr4)/4, where r is the radius of the stem cross-section (Niklas 1992). The stem cross-section of P. crispus is elliptical; hence, I was calculated as I = (π/4)/ab3, where a and b are the shorter and longer axes of an elliptical cross-section, respectively.The flexural stiffness (EI in N m2) was calculated by multiplying E and I and quantifies the stiffness (resistance to bending) of the stem.