CRC Press - Mechanical Engineering Handbook- Mechanics Of Solids Part 3 ppsx

1-20 Section 1 2.Section the truss by making an imaginary cut through the members of interest, preferably through only three members in which the forces are unknowns (assume tensions). The cut need not be a straight line. The sectioning is illustrated by lines l-l, m-m, and n-n in Figure 1.2.24. 3.Write equations of equilibrium. Choose a convenient point of reference for moments to simplify calculations such as the point of intersection of the lines of action for two or more of the unknown forces. If two unknown forces are parallel, sum the forces perpendicular to their lines of action. 4.Solve the equations. If necessary, use more than one cut in the vicinity of interest to allow writing more equilibrium equations. Positive answers indicate assumed directions of unknown forces were correct, and vice versa. Space Trusses A space truss can be analyzed with the method of joints or with the method of sections. For each joint, there are three scalar equilibrium equations, ∑F x = 0, ∑F y = 0, and ∑F z = 0. The analysis must begin at a joint where there are at least one known force and no more than three unknown forces. The solution must progress to other joints in a similar fashion. There are six scalar equilibrium equations available when the method of sections is used: ∑F x = 0, ∑F y = 0, ∑F z = 0, ∑M x = 0, ∑M y = 0, and ∑M z = 0. Frames and Machines Multiforce members (with three or more forces acting on each member) are common in structures. In these cases the forces are not directed along the members, so they are a little more complex to analyze than the two-force members in simple trusses. Multiforce members are used in two kinds of structure. Frames are usually stationary and fully constrained. Machines have moving parts, so the forces acting on a member depend on the location and orientation of the member. The analysis of multiforce members is based on the consistent use of related free-body diagrams. The solution is often facilitated by representing forces by their rectangular components. Scalar equilibrium equations are the most convenient for two-dimensional problems, and vector notation is advantageous in three-dimensional situations. Often, an applied force acts at a pin joining two or more members, or a support or connection may exist at a joint between two or more members. In these cases, a choice should be made of a single member at the joint on which to assume the external force to be acting. This decision should be stated in the analysis. The following comprehensive procedure is recommended. Three independent equations of equilibrium are available for each member or combination of members in two-dimensional loading; for example, ∑F x = 0, ∑F y = 0, ∑M A = 0, where A is an arbitrary point of reference. 1.Determine the support reactions if necessary. 2.Determine all two-force members. FIGURE 1.2.24Method of sections in analyzing a truss. . lines l-l, m-m, and n-n in Figure 1.2.24. 3. Write equations of equilibrium. Choose a convenient point of reference for moments to simplify calculations such as the point of intersection of the. on the location and orientation of the member. The analysis of multiforce members is based on the consistent use of related free-body diagrams. The solution is often facilitated by representing. equations of equilibrium are available for each member or combination of members in two-dimensional loading; for example, ∑F x = 0, ∑F y = 0, ∑M A = 0, where A is an arbitrary point of reference. 1.Determine