The dimensions of (\w\) are force per length. The distribution is of trapezoidal shape, with maximum magnitude w at the interior of the beam, while at its two ends it becomes zero. The moments of inertia of an angle can be found, if the total area is divided into three, smaller ones, A, B, C, as shown in figure below. This load distribution is typical for the beams in the perimeter of a slab. Simply supported beam with slab-type trapezoidal load distribution Simply supported beam with uniform distributed load (UDL) In the following table, the formulas describing the static response of the simple beam under a uniform distributed load w are presented. Either the total force W or the distributed force per length w may be given, depending on the circumstances. The total amount of force applied to the beam is W=w L, where L the span length. The load w is distributed throughout the beam span, having constant magnitude and direction. Simply supported beam with uniform distributed load
![calculate moment of inertia for t beam calculate moment of inertia for t beam](https://i.pinimg.com/originals/ae/ff/8a/aeff8a3671eea9a04f51ebac0a3082a2.png)
The cross section is the same throughout the beam length.
![calculate moment of inertia for t beam calculate moment of inertia for t beam](https://calcresource.com/images/drawing-moment-inertia-tee_xy.rev.e411c06581.png)
The loads are applied in a static manner (they do not change with time).The material is homogeneous and isotropic (in other words its characteristics are the same in ever point and towards any direction).The calculated results in the page are based on the following assumptions: For a simply supported beam that carries only transverse loads, the axial force is always zero, therefore it is often neglected. Typically, for a plane structure, with in plane loading, the internal actions of interest are the axial force N, the transverse shear force V and the bending moment M. The static analysis of any load carrying structure involves the estimation of its internal forces and moments, as well as its deflections. To the contrary, a structure that features more supports than required to restrict its free movements is called redundant or indeterminate structure. These type of structures, that offer no redundancy, are called critical or determinant structures. If a local failure occurs the whole structure would collapse. Therefore, the simply supported beam offers no redundancy in terms of supports.
![calculate moment of inertia for t beam calculate moment of inertia for t beam](https://i.ytimg.com/vi/Ehw-F59kTc4/maxresdefault.jpg)
Obviously this is unwanted for a load carrying structure. Removing any of the supports or inserting an internal hinge, would render the simply supported beam to a mechanism, that is body the moves without restriction in one or more directions. The roller support also permits the beam to expand or contract axially, though free horizontal movement is prevented by the other support. Use Ix and Iy (moments of inertia) to calculate forces and deflections in common steel and wood beams. Use the rectangle shape to calculate the moment of inertia for common wood shapes.
![calculate moment of inertia for t beam calculate moment of inertia for t beam](https://image3.slideserve.com/6305977/slide12-l.jpg)
Both of them inhibit any vertical movement, allowing on the other hand, free rotations around them. I beams, C shapes, T shapes, pipes, rods and channel shapes are common AISC steel and aluminum shapes. It features only two supports, one at each end. This is the focus of most of the rest of this section.The simply supported beam is one of the most simple structures. It is best to work out specific examples in detail to get a feel for how to calculate the moment of inertia for specific shapes. This, in fact, is the form we need to generalize the equation for complex shapes.