A$)$ Overall Structure Free Body Diagram

Given the structural arm loaded perpendicular to its plane as shown below. Explore the section

loads$/$stresses as instructed using the coordinate systems given. The structure cross section is a

solid round. What is shown is the centerline of the bent bar.

Draw an overall FBD for the structure that has been removed from the fixed boundary condition on the left.

Try and show all force arrows in the arrows in the proper direction. Recall in statics we let the math tell us if the arrows are

wrong by a resulting negative sign. We take it to the proper level in design and industry reports where arrows are to be shown

in the correct direction which means fixing equilibrium equations and FBDs$.$ Judiciously use double arrow head convention for

moments $($torque or torsional loads$).$

Overall Structure FBD

D$)$ AA Section Load Equilibrium Equations

Recall the FBD created in step $B$ which isolated or cut the structure at $AA.$

Redraw the AA cut FBD with the following new variables for the complete set of reactions that could be present:

in order axial, shear, moments and torsion labeled as $P_x,V_y,V_z,M_y,M_z,T_x$

Why do you think an engineer would use these particular labels for the loads or stress resultants?

On the following page write all six equilibrium equations for this FBD showing both zero and non$-$zero loads at section

AA$.$

You need not solve these equations just set them up$.$ Identify which of these section loads are zero. Make sure your

arrows are in the correct directions and use the other geometry variables as given in the original sketch.

D contd.$)$ Equilibrium equations for structure cut at AA

E$)$ Sketch Section Outer Surface Stress State

If the arm has a circular cross section sketch the stress states on the projected differential

elements defined below for the AA cross section. Note the center view is looking down the

global X$-$axis. You will sketch these elements on the following pages. Use the local coordinates

given for the stress elements.