**Unformatted text preview: **LAST NAME:
FIRST NAME: Total: / 100 1. The cross-section of a piece-wise homogeneous beam is shown in figure below. For the given geometry
and material properties, compute the following section properties a) Modulus-weighted cross—section area
b) Location of Modulus weighted centroid * c) Modulus weighted moment of inertia [22 (15 points) y El =40 Msi v1 =03
a1 = 5x10'6 ”m”
°F E2 = 10 Msi v2 = 0.25
in/in
°F use ER = 10 Msi a2 = 50 x 10’6 ,.g All dimensions in INCHES , {P r... m/ it”; ‘5'”-—/ «4/ is ~ ,.
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cross-section geometry and location of the centroid are shown in the accompanying figure. For the beam, obtain expressions for the statically equivalent running loads 1% (ﬂap); (90mg (mex Wm); M and mz (X) (24 points) 3. A homogeneous cantilever bearn with unsymmetrical cross—section is subjected to an end force
(parallel to x—direction) and a running load as shown in the figure below. The cross—section dimensions
and location of the centroid are given in the accompanying figure. Obtain expressions for the internal loads P(x),Vy (x),VZ (x),Mx (x),My (x) and M2 (x) (24 points) 1000 lb? Dimensions in INCHES W me [/Wégﬁzo?) n ”la-Q? {bﬂ’i’i is: aw i”; Mm {W M
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4. A homogeneous cantilever beam is subjected to an end load 012% lbs parallel to the z—direction as
shown in the figure below. The material and section properties are defined in the accompanying figure. Compute the free end deflection v0 (20 points) [1:22.311'11!2
[W222.5in4
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52:24.81?
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a=10
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i 19,4 ﬂew m @5325 "mam; ‘L g 5. A cantilever beam with piecewise homogeneous cross—section is subjected to a uniform temperature
change of -100 “F. The material and modulus weighted section properties are listed in the
accompanying figure a) What is the stress at point A on a section at a distance of 10 inches from thgfree end. (17 points)
/ T 1 3:30
0' y* ? E1 :30 Msi 051:5x10_5 mlm
°F
52:10 Msi
. /.
a2=15x10'6 m m
°F
ER=10 Msi
A”=8m2
z: _ 4
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I;=8.67in4
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Fall mm. LAST NAME:
FIRST NAME: Examwéli
M115 l. The cross—section of a piece-wise homogeneous beam is shown in figure below. For the given geometry
and material properties, compute the following section properties
a) Modulus-weighted cross—section area
b) Location of Modulus weighted centroid * c) Modulus weighted moment of inertia Iyy 7/ (15 points) ¥ 0: =5x10‘5 m/in
1 OF
E2 :10 Msi v2 = 0.25
a2=50x10"5 "1”"
°F 2 L34 2, All dimensions in INCHES 2. A cantilever beam is subjected to surface tractions and an end load as shown in the ﬁgure below. The
cross—section geometry and location of the centroid are shown in the accompanying figure. For the ' beam, obtain expressions for the statically equivalent running loads
px (x),py (x),pz (x),mx (x),my (x) and m2 (x). (24 points) Dimensions in INCHES 5
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”mag, blswyl’xclse (”ﬁliéwgéﬂﬂﬁ 3. A homogeneous cantilever beam with unsymmetrical cross-section is subjected to an end force
(parallel to x—axis) and a running load as shown in the figure below. The cross-section dimensions and location of the centroid are given in the accompanying ﬁgure. Obtain expressions for the internal loads
P(x),Vy (30,172 (x),Mx (x),My (x) and M2 (x) (24 points) 1000 [bf ‘Mvog f; g??? «"60 Cﬁwgm) w ‘3‘ were ; z 1
Maw 743W '" ll <7; *ﬁW” 4. A Homogeneous cantilever beam is subjected to an end load of 200 lbs parallel to the y-direction as
shown in the figure below. The material and section properties are defined in the accompanying
figure. Compute the free end deflection wo (20 points) 14:22.31}?
I”, =22.5 in“
22 :114.4 m“
Iyz 224.81%4
, EmlMsi
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WWW WW; i as 7’ 5. A cantilever beam with piecewise homogeneous cross—section is subjected to a uniform temperature
change of —50 °F. The material and modulus weighted section properties are listed in the accompanying
figure ' a) What is the stress at point A 'on a section at a distance of 10 inches from the free end. (17 points} E1230Msi
a =5><10J°' in/in
1 OF
E2=10Msi
a2=15><1046 mun
°F
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I:Z=8.67in4
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mi 2014 LAST NAME:
FIRST NAME: Exam-Ill
£55: me 1. The cross-section of a piece—wise homogeneous beam is shown in figure below. For the given geometry
and materiai properties, compute the following section properties
a) Modulus—weighted cross-section area
b) Location of Modulus weighted centroid a: c) Modulus weighted moment of inertia In (15 points) E1 :40 Msi v1 = 0.3 a =5><10‘E mm”
11 1 OF
E2 = 10 Msi v2 = 0.25
Z ' a:2 =-50><10iG m/m
°F use ER =10 Msi All dimensions in INCHES 2. A cantilever beam is subjected to surface tractions and an end load as shown in the figure below. The
cross—section geometry and location of the centroid are shown in the accompanying figure. For the
beam, obtain expressions for the statically equivalent running loads 1349099.,(x)apz(x)»mx(x)amy (x) and m. (x)- ' (24 points) Dimensions in INCHES
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(parallel to x-direction) and a running load as shown in the ﬁgure below. The cross-section dimensions and location of the centroid are given in the accompanying figure. Obtain expressions for the internal loads P(x), Vy (30,172 (x),'Mx (x) ,My (x) and M2 ()6) (24 points) Y
1000|bf
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i 4. A homogeneous cantilever beam is subjected to an end load of 200 lbs parallel to the x—direction as
shown in the figure below. The material and section properties are defined in the accompanying
(20 points) figure. Compute the free end deflection W0 M 6525‘ A m 22.3 £112 I” a 22.5 in“ IE 2 114.4 m“ Iyz = 24.8 i214 E = lMsi 6 in / in
°F 05:10— M7 it?“ x £62.: Lem g $434.2 {37% Mg; (.59): W 4 {3.25“ {(2%}; ”mm? {km 5. A ca ntiiever beam with piecewise homogeneous cross—section is subjected to a uniform temperature
change of +50 ”F. The materiai and moduius weighted section properties are listed in the
accompanying figure a) What is the stress at point A on a section at a distance of 10 inches from the free end. (17 points) E1 = 30 Msi
0:1 =5x10'6 m/m
°F
E2 =10 MSI
/'
a2 =15><10‘6 m m
°F
ER =10 Ms:
A}: = 81312
1;, =0.67 m“
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- Spring '14
- SureshR.Keshavanarayana