Question 9.3.1: For the frame configurations in Figure 1(a) and Figure 2 det...
DETERMINING STATUS OF A FRAME
For the frame configurations in Figure 1(a) and Figure 2 determine which of these labels apply to each frame: internally unstable, statically determinate, statically indeterminate, or underconstrained.
Frame 1 (Figure 1a): The frame is internally unstable because the force P causes members to rotate, as shown by the ghosted image. A frame in which members intentionally move is called a mechanism. An unstable frame with insufficient boundary conditions to prevent movement is also underconstrained. More members and/or boundary conditions are needed for this frame to be in equilibrium. For example, by changing the pin connection at A to a fixed support, as in Figure 1b, we now have a stable frame that is statically determinate. Alternatively, by adding a diagonal member, as in Figure 1c, we have created a stable frame that is statically determinate.
Frame 2 (Figure 2): The three members are sufficient to form a rigid frame, and removal of a member would make the frame internally unstable. The system has nine unknown loads (F_{Ax} , F_{Ay} , F_{Bx} , F_{By} , F_{Cx} , F_{Cy} , F_{Dx} , F_{Dy} , F_{Ey}) and nine linearly independent equilibrium equations can be written, making it statically determinate.
