A rectangular prism has a rectangular cross section whereas a cylinder has a circular cross section
find the strength of the member subject to bending or shear. Moment of inertia is used to find radius of gyratia or flexural regidity so that member strength flexural stress is found
A cylinder has a circular cross section that is parallel to its base.
Introduction of Arches reduces the bending moment at cross sections due to presence of horizontal force at the support whenever bridge is loaded and thus requirement of cross section is lesser. When triangles are easy to propagate and can have tension/compression only if used as 2-point member in bridges (forces acts only the end of any member not in between), Due to absence of bending moment it also reduces the cross-section requirement. Therefore, if we introduce arches and triangles cross section requirements of each small member get reduced.
trapezoidal cross section
The relation between bending moment and the second moment of area of the cross-section and the stress at a distance y from the neutral axis is stress=bending moment * y / moment of inertia of the beam cross-section
Mass moment of inertia measures an object's resistance to rotational motion due to its mass distribution, while area moment of inertia measures an object's resistance to bending due to its shape and cross-sectional area. Mass moment of inertia depends on both the mass and its distribution, while area moment of inertia depends on the shape and how the material is distributed in the cross-section.
If you are looking to find alternatives for a cross-section design, it is generally recommended to check both the section modulus and the moment of inertia. The section modulus helps determine the resistance of a beam to bending stress, while the moment of inertia indicates the distribution of an area about a neutral axis. Both parameters are crucial for ensuring the structural integrity and efficiency of the design.
radius of gyration = sqrt(Moment of inertia/cross section area) Regards, Sumit
The fully plastic moment of section is referred as the moment at which a given cross-section has reached its yield stress.
section modulus of any section is the ratio of the moment of inertia to the distance of extreem fibre from the neutral axis. plastic section modulus is the section modulus when the cross section is subjected to loading such that the whole section is under yield load. numerically it is equal to the pdoduct of the half the cross section area and the distance of center of gravity of tension and compression area from neutral axis
This is a complex question requiring knowledge of the support connections, the moment of inertia for the cross section, the Young's Modulus, and the slenderness ratio of the member.
direct stress is a stress normal to the cross section, A, and is the result of an axial load, P. direct stress = P/A Bending stress also acts normal to the cross section but varies from tension on one side and compression on the other. and is the result of a bending moment, M. bending stress = Mc/I where I is the area moment of inertia and c the distance from outer fiber to neutral axis
The units of section modulus are typically in terms of length cubed, such as cubic inches (in^3) or cubic millimeters (mm^3), depending on the system of measurement being used. The section modulus is a measure of a beam's ability to resist bending stress and indicates how far the outer edges of a beam are from its neutral axis.
A rectangular prism has a rectangular cross section whereas a cylinder has a circular cross section
moment of inertia is the rotational equivalent of mass. it is given by I= Mk2 moment of inertia in rotational motion play the same role as mass in linear motion, that is in linear motion f = ma while in rotation, torque= I*Angular acceleration where I is the moment of inertia
A cross section in soil is called a soil profile. It shows the different layers of soil and their characteristics from the surface down to the bedrock.