The answer depends of the forces applied to the beam:
- for a single-directional force, the answer is a hollow rectangular shape (with the force applied on the narrow face); an I-beam is the second best.
- For forces applied in two perpendicular directions, the answer is a hollow square section.
- For forces applied from any direction, the answer is a hollow circular bar - a pipe.
Plastic Section Modulus about the element local y-direction
pi x d3 / 32
I think you are refering to the 'section modulus' which is a geometrical property of a cross section. it is the moment of inertia divided by the distance from the centroid or neutral axis to the farthest point of the section. this modulus measures flexural resistance.
This is a technique used by civil and mechanical engineers to calculate the cross section of a geometric figure. It is used to determine the Yield Moment also called My.
Young's modulus is stress/strain. So if the modulus is high, it means that the stress value is greater compare to that of the material where the modulus is low. or in other words, the strain is very less compared to that of the material having low Young's modulus. So it tells that, if a material has high Young's modulus, the material requires more load for deformation of shape (within elastic limit).
Yes, bending stress is directly proportional to the section modulus. A larger section modulus indicates that the cross-sectional shape of the member is better at resisting bending, leading to lower bending stress. Conversely, a smaller section modulus results in higher bending stress for the same applied bending moment.
section modulus is a measure of the strength of a beam. The more the section modulus the more is the strength.
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
Plastic Section Modulus about the element local y-direction
Torssional section module
Sectional modulus of any section determines the strength of a section, i.e. if two sections made up of same material then the section with higher section moduls will carry higher load as the allowable stress is constant for a given material. in analysis of it is useful in determining the maximum stress value to which the section is subjected when the moment is konwn from the relation f=(M/Z) where f= stress at extreem fibre M= maximum bending moment on section Z= section modulus = (moment of inertia/ distance of extreem fibre from NA)
Young's modulus or modulus of elasticity is a property of the material. As in both the wires we have copper material the young's modulus will be the same. It does not get altered with length or area of cross section.
pi x d3 / 32
Section Modulus is moment of inertia divided by distance from center of gravity to farthest point on the cross-section or I/c. The units of Moment of Inertia is distance^4 so the units of section modulus is distance^3 ( distance cubed ). So if your units are in meters: I/c = (m^4)/(m) = m^3
change in shape due to stress applied
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.
The modulus of elasticity is a general term that refers to a material's ability to deform under stress and return to its original shape. Young's modulus, specifically, is a specific type of modulus of elasticity that measures a material's stiffness or resistance to deformation when subjected to tension or compression.