THE UNIVERSITY OF HONG KONG
BACHELOR OF ENGINEERING: LEVEL I EXAMINATION (RE-ASSESSMENT)
DEPART.rviENT OF CIVIL ENGINEERING
STRUCTURAL .rv1ECHAN1CS CIVS1001
May 23 , 2000 9:30am- I 2:30pm (3 hours)
Answer ALL questions
AJI questions carry equal marks.
Use ofElectronic Calculators:
The Calculator: (i) should be silent and battery-operated~
(ii) should not have any printing device, alphanumeric display,
alphanumeric keyboard, or graphic display; and
(iii) should not contain any recorded data or program.
It is the candidate's responsibility to ensure that his/her calculator operates satisfactorily.
Candidates must record the name and type of their calculators ·on the front page of their
examination scripts.
1. The beam in Fig. Q 1 is subjected to a uniformly distributed load of 20kN/m and a point load of
80kN at the free end. The cross section of the beam is symmetrical with respect to the vertical
principal axis and the dimensions are shown in Fig. Q 1.
(a) Draw the bending moment and shear force diagrams. Detennine the bending moments and
shear forces at important locations. Determine the location of the maximum and zero
be?ding moments.
(b) Calculate the maximum flexural stress, crmax, and maximum shear stress, """'-•· Sketch the
corresponding flexural stress distribution and shear stress distribution, and indicate the
locations of the extreme values.
2. (a) A wood beam reinforced by an aluminum channel section is shown in Fig. Q2a. The beam
has a cross section of dimensions 150mm by 250mrn, and the channel has a uniform
thickness of 6mm. If the allowable stresses in the wood and aluminum are 8MPa and
40MPa, respectively, and if their moduli of elasticity are in the ratio 1 to 6, what is the
maximum allowable bending moment for the beam?
(b) A solid circular bar with fixed ends is acted upon by torques 3 To and To at locations shown
in Fig. Q2b. Obtain a formula for the maximum angle of twist of the bar, about its
longitudinal axis.
3. A horizontal load P acts at end C of the bracket ABC shown in Fig. Q3. Point A is pinned
support and B is roller support.
(a) Determine the deflection~ of point C
(b) Determine the maximum upward deflection ~a."t of member AB.
Hints: Assume that the flexural rigidity El is constant throughout the bracket. Also disregard
the effects of axial deformations and consider only the effects of bending due to the
loadP.
4. (a) The cross section of a slit square tube of constant thickness is shown in Fig. Q4a. Derive
the formula for the location of the shear centre from a chosen reference point.
(b) A hollow pipe column AB is fixed at the base and pinned at the top to a horizontal rigid
bar supporting a load of200kN (see Fig. Q4b). Detennine the required thickness t of the
pipe if its outside diameter d is 11 Omrn and desired factor of safety with respect to
buckling is n = 3. The pipe is made of aluminum with E = 72,000:MPa.
5. (a) A generator shaft of hollow circular cross section (outside diameter 200mrn and inside
diameter 160mm) is subjected simultaneously to a torque T = 22.2kNm and an axial
compressive load P = 724kN (see Fig. Q5a). Determine the maximum tensile stress a;,
maximum compressive stress ere, and maximum in-plane shear stress 4ma.- in the shaft.
(b) A beam of rectangular cross section (width b, height h) is made of a material having a
stress-strain curve in tension (see Fig. Q5b) given by the equation:
cr=BrE-B2c (O~&s;~'l:)
where: B 1 and B2 are constants~ and
lina.-< = '1z BriB2.
The stress-strain curve in compression is the same as that in tension.
Derive a formula for the bending moment M if the strains at the top and bottom of the
beam equal E1.
Formulae:
CTx· = 'li (o-x+ CTy) + 'li (~- oy) cos28 + '-"' sin28
Z"xy' = - 'li (CTx- Oj..) Sin2 8 + Z"xy COS2 8
80kN 180
~
r-:
10
I 2m ~
><
I200mm
Cross section
I Fig. Ql
150
lE ~
216
250 I Fig. Q2a
40
..,.., Tv
IFig. Q2b I
I Fig. Q3
3
y 200kN
lm
I Fig. Q4a
IFig. Q4b I
j Fig. Q5a I
I Fig. Q5b I
~--------------~- e
0
END OF PAPER
