課程名稱︰材料力學
課程性質︰必修
課程教師︰施文彬
開課學院：工學院
開課系所︰機械工程學系
考試日期（年月日）︰104/5/12
考試時限（分鐘）：110分鐘
試題 :
Final Exam, Mechanics of Materials, Spring 2015
Time: 10:20 12:10 noon, May 12, 2015.
Please provide details of your calculation. Good luck!
1. (35%) A simply supported W920*449 rolled-steel beam supports loads as shown
in Figure 1. Knowing that σ_all = 160 MPa and τ_all = 100 MPa. Please see
the dimension details of W920*449 on the other page.
(a) Determine the shear force as a function of the position along the beam.
Also, please plot the shear diagram accordingly.
(b) Determine the bending moment as a function of the position along the
beam. Also, please plot the bending moment diagram accordingly.
(c) Determine the maximum value of the normal stress am in the beam.
(d) Determine the maximum value of the principal stress at the junction of
the flange and the web.
(e) Following (c) and (d), whether the specified shape is acceptable as far
as these two stresses are concerned? Why?

2. (30%)
(a) A plate of 2 mm thickness is bent as shown in Figure 2(a). For a
vertical shear of 5 kN, determine the shear stress at the five points
indicated and sketch the shear flow in the cross section.
(b) If the cross section of the beam is built up by assembling plates of 2
mm thickness with nails, as shown in Figure 2(b). This beam is subjected
to a vertical shear of 5 kN. Knowing that the allowableshear force in
the nails is 300 N. Determine the largest permissible spacing of the
nails along thebeam length.

3. (35%) The situply supported beam AC rests on the cantilever beam DE, as shown
in Figure 3(a). Thecross section of the beam DE is shown in Figure 3(b).
(a) Determine the shear force as a function of the position x_1 on beam AC.
(b) Determine the bending moment as a function of the position x_1 on the
beam AC.
(c) On the beam DE, use singularity functions to describe the shear force
and bending moment in terms of x_2. Also, please draw the shear diagram
and bending moment diagram along the beam DE.
(d) At point E, please sketch the shear flow on the cross section of the
beam.
(e) Following (d), determine the location of the location of the shear
center O.