Mae 241 - Lec9

MAE 241 - Statics Summer 2009

Dr. Konstantinos A. Sierros Office Hours: M and W 10:30 – 11:30 (263 ESB new add) [email protected] Teaching Blog: http://wvumechanicsonline.blogspot.com

The train car has a weight of 24 000 lb and a center of gravity at G. It is suspended from its front and rear on the track by six tires located at A, B, and C. Determine the normal reactions on these tires if the track is assumed to be a smooth surface and an equal portion of the load is supported at both the front and rear tires.

The 1.4-Mg drainpipe is held in the tines of the fork lift. Determine the normal forces at A and B as functions of the blade angle θ and plot the results of force (vertical axis) versus θ (horizontal axis) for 0 < θ < 90°.

The horizontal beam is supported by springs at its ends. Each spring has a stiffness of k = 5 kN/m and is originally unstretched so that the beam is in the horizontal position. Determine the angle of tilt of the beam if a load of 800 N is applied at point C as shown.

6: Structural analysis

Chapter objectives • Determine the forces acting on truss members • Analyze forces acting on frames and machine members

6.1 Simple trusses • A truss is a structure composed of slender members joined together at their end points • Planar trusses lie in a single plane and used to support roofs and bridges • The roof load is transmitted to the truss at the joints by means of a series of purlins

6.1 Simple trusses

Load on the deck transmitted to stringers, then to floor beams and finally to the joints of the two supporting side trusses Why use a rocker/roller at one end of bridge?

6.1 Simple trusses Assumptions for design How do we design member and connections of trusses? - First need to determine the forces developed in each member when the truss is subjected to loading We have to make two assumptions 6. All loadings are applied at the joints 7. The members are joined together by smooth pins

6.1 Simple trusses

Because of the previous two assumptions • Each truss member will act as a two-force member • Tensile forces tend to elongate members • Compressive forces tend to shorten members • Compression members must be made thicker than tension members

6.1 Simple trusses

adding members CD and DA

6.2 The method of joints The method is based on the fact that the entire truss is in equilibrium • Draw the free body diagram of each joint • Use the force equilibrium equations (ΣFx = 0, ΣFy = 0)

6.3 Zero-force members • There may be truss members that support no loading. These are zeroforce members and are used to increase the stability of the truss during construction and to provide added support if the loading is changed

6.4 The method of sections • If we need to find the force in only a few members of a truss, we can analyze the truss using the method of sections • If the truss is in equilibrium, any segment of the truss is also in equilibrium

6.4 The method of sections

6.4 Space trusses • A space truss consists of members joined together at their ends to form a stable 3D structure • The simplest form of a space truss is a tetrahedron