Civil PE Sample Examination Third Edition
Michael R. Lindeburg, PE
Professional Publications, Inc. • Belmont, California
33
Afternoon Session Structural . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .
121. A two-lane highway bridge is constructed using
precast concrete girders. The girders are simply supported and span 60 ft. The weight of girders and deck is such that the dead load bending moment at the critical location for bending moment is 500 ft-kips. If the bridge is designed for AASHTO HL-93 loading using LRFD strength criteria, and only one lane is loaded at a time, and if girder load distribution is not considered, the design bending moment per lane at the critical location is most nearly
lines 1, 2, and 3. Disregard accidental torsion that may be required by code. The axial compression and tension forces in the shear wall boundary members at line 2 under the given loadings are most nearly 1
2
100 ft
60 ft
3
24 ft
(A) 2500 ft-kips (B) 3000 ft-kips
54 ft plywood diaphragm
(C) 3500 ft-kips
N
(D) 4000 ft-kips 122. A rigid diaphragm transfers a lateral wind force
of 0.4 kip/ft into a system of shear walls whose relative rigidities, in multiples of R , against forces in the north direction are shown in the plan. The force in wall A of the system is most nearly 120 ft
300 lbf/ft
(A) 10 kips (B) 12 kips (C) 16 kips
40 ft
(D) 20 kips
wall B (R )
60 ft
240 lbf/ft
wall D (3R )
wall A (4R )
wall C (R )
124. For the truss shown, the modulus of elasticity for
wall E (3R )
all members is 29,000 ksi. The cross-sectional area of the members is 8 in2. The horizontal deflection at joint D of the truss is most nearly D
N
0.4 kip/ft
C 20 ft
30 kips
(A) 15 kips
10 ft
(B) 22 kips
B
A
(C) 27 kips (D) 33 kips 123. The roof framing of a single story commercial
building consists of wood joists supported by timber beams and sheathed with a properly nailed and blocked plywood diaphragm. Seismic lateral forces for NS ground motion are shown. Assume sufficiently rigid plywood shear walls 14 ft high and 24 ft long are constructed at
15 ft
(A) 0.01 in (B) 0.02 in (C) 0.04 in (D) 0.08 in
P P I
*
w w w . p p i 2 p a s s . c o m
34
C I V I L
P E
S A M P L E
E X AM I NA TI ON
125. A two-story building is 14 ft from ground to
127. A continuous 8 in thick bridge deck is made of
second floor and 12 ft from second floor to roof. The exterior wall projects 3 ft above the roof level to create a parapet. The exterior wall weighs 15 psf, the second floor dead load is 30 psf, and the roof dead load is 20 psf. The building is wood framed with plywood diaphragms and shear walls resisting all lateral forces. The building is situated in seismic performance category D, where the design spectral response acceleration at short periods is 0.6, the design spectral response acceleration at one second period is 0.2, and the importance factor for seismic response is 1.0. Assume the building qualifies as a building frame system with light-frame walls with shear panels. The seismic base shear for north-south (NS) ground motion by the IBC static force procedure, on a working load basis, is most nearly
reinforced normal weight concrete. It is supported by steel girders spaced 8.5 ft on center, with flange widths of 1 ft. The positive bending moment, per foot of width, for dead weight of the slab is 1.0 ft-kip/ft, and is 0.3 ft-kip/ft for a future wearing course. The deck is continuous over three or more spans and is to be designed by the traditional approach using the AASHTO LRFD Bridge Design Specifications . The factored positive bending moment per foot of deck width that controls deck strength is most nearly
8 in 1
2
120 ft
1 ft (typ.) 8.5 ft 60 ft plywood diaphragm
(A) 8 ft-kips/ft
N
(B) 10 ft-kips/ft (C) 12 ft-kips/ft (D) 14 ft-kips/ft
(A) 25 kips (B) 45 kips
128. The circular shaft shown is subjected to an axial tension force P at its free end and a compressive force of
(C) 65 kips (D) 80 kips 126. The compound beam shown has an internal hinge (M = 0) at point B and is simply supported on
50 kips at point B. Note that the shaft is hollow between points A and B. The allowable normal tension stress is 22 ksi, the modulus of elasticity is 29,000 ksi, and the maximum allowable elongation is 0.04 in. The maximum allowable value of P is most nearly
hinges or rollers at points A, C, and E. The ordinate of the influence line for the bending moment at point D, which is 12 ft to the right of support C, is most nearly A
C
B
8 ft
8 ft
D
12 ft
A
50 kips 20 in
5 ft
C
B
P
E
8 ft
0.75 in
3 in
30 in
(A) 111 kips (B) 117 kips
(A) 1 ft-kip/kip (B) 3 ft-kips/kip
(C) 155 kips (D) 171 kips
(C) 5 ft-kips/kip
129. A beam is simply supported over a 22 ft span and
(D) 7 ft-kips/kip
overhangs the left support 8 ft. Uniformly distributed dead loading of 2 kips/ft and live loading of 3 kips/ft are applied. The live load is positioned to produce
P P I
*
w w w . p p i 2 p a s s . c o m
105
Solutions Afternoon Session Structural . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .
121. The HL-93 consists of an HS20-44 design truck
combined with a 640 lbf/ft lane load. The resultant of the three wheel loads for an HS20-44 loading is a 72 kips force located 4.67 ft from the 32 kips center force. x ¼
åP i x i R
ð32 kipsÞð14 ftÞ þ ð8 kipsÞð28 ftÞ 72 kips ¼ 9 33 ft ¼
:
Maximum wheel-load bending moment occurs when the midspan lies halfway between the resultant and the central 32 kips force. Thus, the position for maximum wheel-load bending moment is
The maximum moment due to the lane loading is
kip 0 640 ð60 ftÞ2 2 ft wL ¼ M LL ¼ 8 8 ¼ 288 ft-kips :
The AASHTO specification requires an increase in the wheel-load bending moment to account for dynamic loading, but this is not applied to the dead or lane loading. A multiple presence factor, MPF, is required when only one lane is loaded. IM ðdynamic load allowanceÞ ¼ 0 33 :
MPF ðmultiple presence factorÞ ¼ 1 2 :
DC ðcomponent dead load factorÞ ¼ 1 25 :
14 ft
14 ft
LL ðlive load factorÞ ¼ 1 75 :
32 kips
32 kips
8 kips
M u ¼ ðDCÞM D þ ðLLÞðMPFÞ
R
A
B 9.33 ft
¼ ð1 25Þð500 ft-kipsÞ þ ð1 75Þð1 2Þ :
(0.5)(4.67 ft)
30 ft R A
M LL þ ð1 þ IMÞM truck :
:
288 ft-kips þ ð1 þ 0 33Þð807 ft-kipsÞ :
R B
60 ft
¼ 3483 8 ft-kips
ð3500 ft-kipsÞ
:
The answer is (C).
Maximum wheel-load bending moment from the truck occurs under the 32 kips load to the right of midspan.
R A ¼
V ¼ w L ¼
årF L
kip 04 ð160 ftÞ ft :
¼ 64 kips
ð72 kipsÞ 30 ft þ ð0 5Þð4 67 ftÞ :
¼
122. The resultant lateral force is
This resultant force acts 80 ft from the west wall. The center of rigidity of the wall group is
:
60 ft
¼ 38 8 kips :
M truck ¼
årF ¼ ð38 8 kipsÞ 30 ft þ ð0 5Þð4 67 ftÞ :
ð32 kipsÞð14 ftÞ ¼ 807 ft-kips
:
:
åR i x i åR i 4 R ð0 ftÞ þ 3R ð120 ftÞ þ 3R ð160 ftÞ ¼ 4R þ 3R þ 3R ¼ 84 ft ½from the west side of wall A
x ¼
P P I
*
w w w . p p i 2 p a s s . c o m
106
C I V I L
P E
S A MP L E
E X A MI NA TI ON
(This disregards the accidental torsion of 5% that may be required by code or ASCE7.)
L V
�
�
24 ft
21 kips
From symmetry, h
y ¼ 30 ft
�
14 ft
½from the south wall T
The wall system is subjected to a torsional moment of elevation of wall on line B
L
2 160 ft ¼ ð64 kipsÞ 84 ft
M t ¼ V x
C
The overturning moment on the wall is
2
M OT ¼ V h
¼ 256 ft-kips ½clockwise
¼ ð21 kipsÞð14 ftÞ ¼ 294 ft-kips
The polar moment of inertia for the walls resisting the torsional moment is
The axial force in the shear wall boundary members is J ¼
åðR yi x 2i þ R xi y 2i Þ 2
¼ 4 R ð84 ftÞ þ 3R ð120 ft 84 ftÞ
T ¼ C ¼
2
294 ft-kips 24 ft ¼ 12 3 kips ð12 kipsÞ
þ 3R ð160 ft 84 ftÞ2
¼
þ R ð30 ftÞ2 þ R ð30 ftÞ2 ¼ 51 240R ft
:
2
;
The answer is (B).
The maximum lateral force resisted by wall A is the combined direct force plus the force caused by the torsional moment, both acting in the same sense. V A ¼
¼
124. Using the dummy load method, the unit virtual
force is applied at D in the direction of the required deflection.
M R x 4R V þ t i i J åR yi
D
4 ð64 kipsÞ þ ð256 ft-kipsÞ4 ð84 ftÞ :
D
R 51 240R ft 2
R 10R
¼ 27 3 kips
M OT L
C
;
ð27 kipsÞ
20 ft
C 20 ft
30 kips 10 ft
The answer is (C).
10 ft B
A
and the lateral forces transfer to the shear wall on the basis of their tributary width. Thus, the lateral force acting on the shear wall at line 2 is V ¼
ft ¼ 21 000 lbf ;
P P I
*
w w w . p p i 2 p a s s . c o m
ft
2
load system Q
The member forces for the real loads, load system P , and for the dummy load system, system Q , are found using basic statics. N P
2 ð21 kipsÞ
15 ft
load system P
åwB
lbf 100 ft þ 300 lbf 60 ft ¼ 240
B
A
15 ft
123. The plywood diaphragm is considered flexible,
1 lbf
member AB AC AD BC CD
(kips) 15.0 25.0 0 25.0 0
N Q
(lbf) 1.0 0 1.33 – 1.67 – 1.67
L
N P N QL
(in) 180 150 240 150 150
(kips-lbf-in) 2700 0 0 6263 0 8963
