![]() Indeed, centroidal axis x, lies at a distance equal to h/2-t_f/2 from the parallel axis through the sub-area A centroid (and the same distance from sub-area C centroid too). Therefore, the parallel axes theorem should be employed for these two sub-areas (later in text, a short introduction on the parallel axes theorem is given). This axis happens to also be centroidal for the rectangular sub-area B, however the same is not true for sub-areas A and C. Let's consider here, the moment of inertia around the centroidal axis x, of the z-section, which is parallel to the two flanges. ![]() See our article on finding the moment of inertia of compound shapes for more details on the methodology. It is important however that the individual moments of inertia I_A, I_B, I_C, have to be determined around the same axis, before such a summation can be made. However, the end result should be the same if the methodology is followed consistently. Substituting these values into our square beam bending stress equation, we get: 6 × M / a³. ![]() Say a square beam has a side measurement, a, of 0.10 m and experiences a 200 N·m bending moment. It is perfectly possible to split the given z-section in many different ways. To find the bending stress of a square beam, you can use the following equation: 6 × M / a³. The wanted moment of area I of the entire z-section, around a specific neutral axis, can be considered as the additive combination of I_A+I_B+I_C, of the individual moments of the sub-areas, over the same axis. ![]() Sub-areas B, C are identical in terms of sectional area, each having a width equal to b_f=b-t_w. Sub-area B accounts for the entire web (including the two small areas where flanges and web interesect), while sub-areas A and C account for the remaining flange parts, (A for the upper flange and C for the lower one). In the previous chapter we found that if a great many forces are acting on a complicated mass of particles, whether the particles comprise a rigid or a nonrigid body, or a cloud of stars, or anything else, and we find the sum of all the forces (that is, of course, the external forces, because the. The moment of inertia of a z-section can be found if the total area is divided into three, smaller ones, A, B and C as shown in figure below. ![]()
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