TaxOnFear said:Where are your workings? Where is it you're having problems?
Yes, Z= I/(d/2), so what is I in terms of the base (b) and height (d), for a rectangular cross section?mm391 said:Z= I/y with y being depth/2.
But I can't see how this will help. Sorry.
PhanthomJay said:Yes, Z= I/(d/2), so what is I in terms of the base (b) and height (d), for a rectangular cross section?
you mean (bd^3/12)/(d/2) = b*d^2/6mm391 said:Firstly thank you for your help and patience.
((b*d^3)/(d/2)
No, you have 2 unknowns and 2 equations...the one that was given you...in your original post..Z = b*d^2/6
Z * 6 = b*d^2
But I still have two unknowns and one equation.
To calculate the dimensions of a rectangular beam, we will need to use the formula F = M*y/I, where F is the force (in Newtons), M is the bending moment (in Newton-meters), y is the distance from the neutral axis to the outermost fiber (in meters), and I is the moment of inertia (in meters^4). We can rearrange this equation to solve for y, which will give us the height of the beam. Then, we can use the formula V = (b*h^2)/6, where V is the volume (in cm^3), b is the width of the beam (in cm), and h is the height of the beam (in cm). Finally, we can use the formula σ = M*c/I, where σ is the stress (in MPa), c is the distance from the neutral axis to the centroid (in meters), and I is the moment of inertia (in meters^4). We can rearrange this equation to solve for c, which will give us the distance from the neutral axis to the centroid. Once we have the height, width, and distance from the neutral axis to the centroid, we can calculate the remaining dimensions of the rectangular beam.
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. In the context of a rectangular beam, it is a measure of how the beam's cross-sectional area is distributed around its neutral axis. The larger the moment of inertia, the more resistant the beam will be to bending. Therefore, a larger moment of inertia will result in smaller dimensions for a given bending moment, as the beam will be able to withstand the force more easily.
The bending moment is the force that causes a beam to bend or flex. In order to withstand this force, the dimensions of a rectangular beam must be large enough to distribute the force and prevent the beam from breaking. A larger bending moment will require larger dimensions for the beam in order to maintain its structural integrity.
There is no hard and fast rule for the maximum dimensions of a rectangular beam. The appropriate dimensions will depend on various factors such as the load, the material of the beam, and the structural requirements of the application. To determine the appropriate dimensions, it is best to consult with a structural engineer who can analyze the specific requirements and provide a suitable design for the beam.
The calculations for determining the dimensions of a rectangular beam are specific to its shape. Other beam shapes, such as circular or triangular, will have different formulas and considerations for calculating their dimensions. It is important to use the appropriate formulas and consult with a structural engineer for the design of any type of beam.