if the beam is truly fixed against rotation at both ends, max deflection occurs at midpoint and is equal to PL^3/192EI , or near an inch and a half for your load and beam length and size. But, you have to be careful using long channels because stresses may be excessive if the beam is not laterally supported against local flange buckling, and loading not at the shear center causes additional torsional and warping stresses. If the beam is simply supported, stresses double and deflection increases fourfold. Seems like a very flimsy channel to use for this loading. Allowable stress is a great concern.blake92 said:i have a 20.5ft c3x5 steel channel with a point load at the exact center and i wanted to determine its maximum deflection.
the point load is 921.86lbs, and moment of inertia is 1.86in^4.
modulus of E= 30,000,000psi
The formula for calculating the deflection of a fixed beam with a point load at the center is:
δ = (FL^3)/(48EI), where δ is the deflection, F is the point load, L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia.
The point of maximum deflection in a fixed beam with a point load at the center is located at the center of the beam. This is because the point load causes the beam to bend downwards, and the center is the furthest point from the fixed supports on either end.
Yes, the deflection of a fixed beam with a point load at the center can be reduced by increasing the stiffness of the beam. This can be achieved by using a material with a higher modulus of elasticity, increasing the beam's moment of inertia, or decreasing the length of the beam.
A fixed beam is one that is rigidly attached to supports on both ends, while a simply supported beam is supported on both ends but can rotate or move freely. This means that a fixed beam can resist both vertical and horizontal forces, while a simply supported beam can only resist vertical forces.
Yes, the calculation of deflection for a fixed beam with a point load at the center assumes that the beam is linearly elastic and that the material is homogenous and isotropic. It also assumes that the beam is loaded within its elastic limit and that the deflection is small compared to the beam's length.