浙江工业业大学材料力学考研样卷3

Material Mechanics Examination
2003-2004 Second Term
Class： Number： Name： Score： . 1.(15 points) A wooden truss is subjected to a force P shown as following. Known: P＝80kN, the allowable tensile and compressive stress [σt]=8MPa，[σc]=10MPa. Determine the cross-sectional areas of bar AB and CD. (Neglect stability).
2. (15 points) The T-shape Beam as shown in the Figure, Known: the allowable tensile stress [σt]＝60MPa，the allowable compress stress [σc]＝200MPa. Check the strength of the beam。

（I z ＝763㎝4, |y
1
|=52mm）
2
=6kN
mm）
3. (15 points) For the stress element in the figure. (1) Find the shear stress and normal stress in the inclined area; （2）Find the principal stress and its direction; (3)plot the principal plane in the stress element.
30
4. (15 points) A hollow shaft with outer diameter D ＝200mm and inner diameter d ＝160mm. Known ：P ＝60kN, the allowable stress [σ]＝80MPa ，l ＝500mm 。

(1) Check the strength of this shaft; (2) Show the risky point in the figure; and (3) plot the stress element of the risky point.
5.(10 points) Find the critical load F cr and the critical stress σcr . Known: the coefficient of effective length μ=1, hollow column with outer diameter D=52mm and inner diameter d=44mm ，the length L=950mm, the tensile limit MPa b 1600=σ, the proportional limit
MPa
p
1200=σ
，E=210Gpa.
F
F
6. (15 points) A weight P is dropped onto the simple beam AB, as shown in the figure, from a height h. Determine the maximum normal stress of the beam and the vertical deflection at the middle point of the beam. Given: E, I, W.
7. (15 points) A beam and a bar are shown as the following. Given: q, L, the flexural rigidity EI of the beam ABC, the constant E and the cross-sectional area A of the bar BD. Find the axial
force of the bar BD and the vertical deflection at point B of the beam.
Appendix ：Common Equations of M. M 1、Tension and Compress: σ=A
N ；EA
Nl l =
∆。

2、Torsion ： P I T ρτρ=，t
W T =max τ；P
GI
Tl =
φ，P
GI
T =
ϕ，n
W m
9549
=。

3、Bending ：Z
I My =
σ，W
M max max =
σ；b
I QS
Z Z
*=
τ；
EI
M dx
v d =2
2
；
D
Cx d d EI
M x x ++=
⎰⎰
)(
ν 。

4、Stress status ： ατασσ
σσ
σα2sin 2cos 2
2
xy y
x
y
x
--+
+=
，y x xy
tg σ
στα--
=220，
ατασσ
τα2cos 2sin 2
xy y
x
+-=
；
2
2
min
max )2
(
2
xy
y
x
y
x
τσσσσ
σσ+-±+=⎭
⎬⎫，
4、Combined Bending with Torsion ：
3rd strength theory:
[]σ≤+2
2
1T
M
W ，[]στσ≤+2
24； 4th strength theory:
[]σ
≤+22
75.01T
M
W
，[]στ
σ≤+2
2
3。

5、Castigliano ’s theorem ：⎰
∂∂=l
x
i
i d P x M EI
x M )()(δ， ∑
=∂∂=
n
j j
j
j j j i P N
EA l N 1
δ
6、Unit-load method ：⎰
=
∆l
x
EI
d x M x M )()(， ∑
==
∆n
i i
i i i EA l N N 1
， ⎰
=
∆l
P
x
GI
d x T x T )()(
7、Impact ：Free falling st
d Q T K ∆++=211；Horizontal impacting st
d g K ∆=2
ν
8、Stability of Columns ：A
I i =
，i
ul =
λ，22
)
(l EI
P Cr μπ=
， 2
2
λ
πσE cr =
，σ
πλE P 2
=
，
b
a s
s σλ-=
; st
cr n p
P n ≥=
9、Deflections and slopes of Beams。