1.For a cantilever beam loaded in bending, prove that b = 2_3 for the
Sb_r guidelines in Fig. 2–19. 2. Consider a tie rod transmitting a tensile force
F. The corresponding tensile stress is given by
σ
=
F/A, where
A
is the area of the cross section. The deflection of the rod is given by Eq. (4–3), which is
δ
=
(Fl)/(AE), where
l
is the length of the rod. Using the Ashby charts of Figs. 2–16 and 2–19, explore what ductile materials are best suited for a light, stiff,
and
strong tie rod.
Hint:
Consider stiffness and strength separately
1. Sketch a free-body diagram of each element in the figure. Compute the magnitude and direction of each force using an algebraic or vector method, as specified.
2.For the beam shown, find the reactions at the supports and plot the shear-force and bending moment diagrams. Label the diagrams properly and provide values at all key points.
