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Structural Engineering Mechanics and Materials Department of Civil and Environmental Engineering, University of California at Berkeley
Spring Semester 2014
Preliminary Examination- Design Question Important Note: All the information needed to do this problem are given below. If you still think there is an item that you need and is not given, or an equation that you need to use but do not remember, please make an assumption, explain your assumption and use your assumed value or equation and continue your solution. No questions can be asked or answered during this exam. Design the frame shown below for the applied loads. The dead load DL, live load LL and seismic lateral load Q shown on the sketch below are all unfactored nominal values. Use load combinations that you think are appropriate for this case. The steel girder has lateral bracings and lateral-torsional buckling of the steel beam is not a consideration. You need to select appropriate material properties of steel and concrete in your design.
Please make sure to check ALL applicable failure modes and if you do not have equations to check any failure mode, explain how you would do it if this was an open book exam.
30 ft.
DL=3,000 kips
Rectangular R/C Column to be designed
LL=100 kips
24 ft.
Q=30 kips
Steel I-Beam to be designed. See cross section below.
1 inch thick plate (height of plate to be calculated) PL 12”x1”
Steel Beam Section
University of California at Berkeley Structural Engineering Mechanics and Materials
Department of Civil and Environmental Engineering Fall Semester 2012
Doctoral Preliminary Exam- Fall 2012 Design
______________________________ Consider the tower crane shown in Figure 1. You need to answer the following questions:
Question 1. Check the design of the steel “jib” (the front arm of the crane) and design the reinforced concrete tower for the given load condition in Fig. 1 as well as for the condition of no live load (only 30 kips dead load is present). The given loads are nominal (un-factored) loads. The jib structure is a 4-legged truss system with all horizontal, vertical, and diagonal members consisting of HSS2.5x1/4 pipe section with exterior diameter of 2.5 inches and thickness of 0.25 in, as shown in Figure 2. The cross section area of a single pipe section is 1.66 in2. The weight per foot of the 2.5” pipe is 6 pounds. The reinforced concrete tower has circular cross section. To prevent cracks in the R/C tower during frequent use of the rotating jib, you need to design it such that the maximum tensile stress in the concrete under the factored combination of dead and live load does not exceed 200 psi. The moment of inertia of a circular cross section is I = (R4)/4 where R is the radius.
Question 2. Consider the crane not having any lift load and position of the jib raised to 60o as shown in Figure 3. The crane in this position is subjected to high winds of a hurricane. The winds are from left to right. a. Calculate maximum wind pressure in pounds per square foot of the exposed vertical surface of the jib that can cause the jib to rotate clockwise in the plane of the paper and collapse as shown in Figure 4 (photos are from Hurricane Sandy in New York). b. In your opinion, what should have been done before Hurricane Sandy made a landfall to ensure that the tower crane jib on Figure 4 would not collapse?
Please read this important note before you start the exam
All the essential information is given. Any other information that you think you need, such as say strength of concrete or steel used, are part of this design
problem. You need to make assumptions on any number you need and explain your assumptions. No questions can be answered during this exam.
Figure 1 for Question 1
10 ft.
65 ft.
60 ft.
30 kips
7 ft.
Steel Jib to be checked
R/C Tower to be designed
5 kips
Figure 2- Details of Steel Jib
All truss members are HSS2.5x1/4: Area=1.66 in2 External Diameter = 2.5 in. Thickness= 0.25 in. Fy= yield stress= 80 ksi Weight per foot= 6 pounds per foot
Elevation Cross Section
2 ft
2 ft
2 ft.
2 ft.
Figure 3 for Question 2
30 kips
Wind
Figure 4 for Question 2
Wind
Wind
1
University of California at Berkeley Structural Engineering Mechanics and Materials Department of Civil and Environmental Engineering
Doctor Preliminary Exam – Design - Spring 2012
The bridge structure shown in figure 1 is considered. The two columns of the bridge: (i) are fixed to the deck and to the footings, and (ii) have the same hollow square section. Our aim is to design and determine the response of the bridge under the combined effect of earthquake loading in the North-South direction and gravity loads. The uniformly distributed factored load, w, includes the self weight of the deck, the permanent loads, half of the weight of the columns as well as the live load contributing to the seismic load. The design elastic acceleration at the first translational mode of vibration is Sa = 0.8g. Use a response modification factor R = 3 to obtain design forces. The yield strength of steel used is fy = 60 ksi with a post-yield hardening ratio of 2%, as shown in figure 1(d). The concrete compressive strength is fc
‘
= 6 ksi. Consider the RC sections to be well confined. The columns have adequate capacity against buckling and the pile foundations fixed to the ground. Ignore nonlinear geometry (P-D) effects. (1) Check if the column section has adequate flexural strength. The longitudinal (flexural) steel ratio of the reinforced concrete (RC) columns is L = 1.5%. The longitudinal steel ratio is defined as the total area of longitudinal steel used divided by the gross section area.
(2) What is the peak moment the columns can develop at their base?
(3) Determine whether the columns have adequate shear strength. For the RC column the shear reinforcement of each segment of the column consists of two No. 6 bars every 8 inches, see fig. 1(c).
(4) Calculate the relative displacement, y, of the deck (in the North-South direction) with respect to the ground when the maximum tensile strain of the section of the columns at their base reaches the yield strain of steel in tension.
(5) If instead of pile foundations we use shallow square foundations of B=30 ft and D =7 ft, see Figure 1(a), calculate the horizontal absolute acceleration of the deck corresponding to initiation of foundation uplift. Assume that the soil stresses on the shallow footing base due to gravity are uniform. Are the shallow foundations going to uplift during a design-level earthquake excitation? The bearing stress capacity of the soil is s = 0.08 ksi.
(6) What is the peak tensile strain and what the peak compressive strain of the section of the column at its base when the relative displacement of the deck (in the North-South direction) with respect to the ground is y?
You only need to do either steel or reinforced concrete design of the columns but not both!
2
w =14 kips / ft
150 ft
infinitely stiff deck Column fixed to the deck
50 ft
150 ft 150 ft
7 ft
Dstiff square reinforced concrete pile cap
frictionless roller
REINFORCED CONCRETE DESIGN
Uniformly distributed longitudinal steel with
L = 1.5%
North
t=18 in.
(d) stress-strain relation of (reinforcing) steel
10.02
stress
strain
fy = 60 ksi
E =29000 ksi
North
No. 6 @ 8 ‘’
Lc = 96 in.
Lc = 96 in.
ground
pile
(a) Side elevation view of the bridge
(b) Section of steel column
(c) Section of RC column
B
t=4 in.
STEEL DESIGN
Lc = 32 in.
Lc = 32 in.North
Figure 1.
University of California at Berkeley Structural Engineering Mechanics and Materials
Department of Civil and Environmental Engineering Fall Semester 2011
Doctoral Preliminary Exam- Spring 2011
Design ______________________________
The objective of this problem is to check the design of the steel pipe tower and to design the R/C foundation. In addition you are asked to sketch the connection of the steel pipe tower to the R/C foundation, but you do not need to design this connection.
Given the information below and in the next page, do the following:
1. Establish the design seismic force acting at the center of the spherical tank using the response spectra shown below. The weight of the tank is given as W= 100 kips. Ignore the self weight of the steel pipe tower.
2. The steel tower is a hollow steel pipe with outside diameter of 48 inches and inside diameter of 46 inches with a thickness of 1.0 inch. Check the design of the pipe under the combination of gravity and seismic load. For combination of axial load and bending moment in steel, you can use the following interaction equation:
Pu/φcPc + (Mu/ φbMp)2 ≤ 1.0
3. Show the details of the base connection of the tower to the foundation in a neat sketch. Do not design this connection.
4. Design the R/C foundation for the tower assuming a square spread footing. Assume the supporting soil to be rock with ultimate bearing strength of 220 kips per square feet.
5. Establish what will be the horizontal movement of the center of the water tank, Point “A”, under seismic load.
Important Note: All the essential information are given. Any other information that you think you need , such as say strength of concrete or steel used, are part of this design problem . You need to make assumptions on any number you need and explain your assumptions. No questions can be answered during this exam.
ELEVATION
1. Hollow Steel Pipe to be designed
3. R/C Foundation to be designed
70 ft
W = 100 kips
E
2. Base Connection to be sketched not designed
A
ROCK
Pipe: d = 48 in. d1 = 46 in.
University of California at Berkeley Structural Engineering Mechanics and Materials
Department of Civil and Environmental Engineering Fall Semester 2010
Doctoral Preliminary Exam- Fall 2010
Design______________________________
The objective of this problem is to design a retrofit for a beam to increase its load carrying capacity. Given the information here and on the figure below do the following:
1. Check the beam in “as is” condition and establish how much concentrated load it can take at midspan.
2. Consider the retrofit scheme shown below using cables and vertical stubs at L/3 points and design the cables such that the beam can take twice as much as the capacity you established in Step 1 above.
For both steel and concrete for beam-column interaction equation use: P/Pcr + (M/Mp)2 =1.0. For buckling capacity you can use Euler’s equation. For other items, such as material properties etc., make assumptions and please provide a brief justification for all your assumptions. Show all your calculations.
B
R/C Beam Cross Section
# 6 stirrups @ 8 inch spacing
8 ft.
6 # 14 bars on each side.
8 ft.
5 ft.
t =2 in.
5 ft.
Steel Beam Cross Section
2 parallelcables
Steel or R/C Beam
You only need to do either steelor R/C beam but not both!
A
A
30 ft
P
15 ft B
Beam in “As-Is” condition before
retrofit
10 ft 10 ft 10 ft
30 ft
15 ft
Beam After retrofit
2P
5 ft Roller
UNIVERSITY OF CALIFORNIA, BERKELEY Department of Civil and Environmental Engineering SPRING SEMESTER 2009 Structural engineering, Mechanics and Materials Name: ____________________________________
Ph. D. PRELIMINARY EXAMINATION
DESIGN Design the main box girder of the cable stayed bridge shown below either in “Steel” or “Reinforced Concrete”. The bridge is a pedestrian/bike bridge. The deck of the bridge is a 10-inch thick reinforced concrete slab. The design of deck slab is not part of this problem. The width of the deck is 20 feet made of two 10-feet wide lanes. For each case of “Steel” or “Reinforced Concrete” the box girder has the same outside dimensions of 8ftx4ft as shown below. The box is a double-cell box with all walls having the same thickness. You need to select the material used in the box as well as thickness of the box walls as part of your design. If you are doing R/C option, you need to design the reinforcement in the box walls as well. Consider only combination of dead load (self weight) and live load in your design. Wind and seismic loads are not part of this problem. Light weight concrete (110 lb/ft3) is used in the deck. The weight of each guardrail and median divider is 200 pounds per linear foot of the bridge. The live load acting on the surface of the deck is 300 pounds per square feet of the deck. Notice that live load is not necessarily applied to the entire surface of the deck. In design of the box girder, consider all applicable strength-related limit states (i.e. failure modes). Deflection limit states are not part of this problem. Use the interaction equation: P/Pcr + (M/Mp) 2 ≤1.0 for both steel and concrete boxes. For buckling capacity you can use Euler’s equation: Pcr = (π2EA) / (KL/r) 2 ≤ Pmax , where Pmax is equal to AgFy for steel box section and (0.8)[0.85f’c(Ac-Ar)+FyrAr] for concrete section. Make assumptions on any information that is not given, such as concrete cover on rebars and material properties of steel and concrete, and explain your assumptions. Show all your calculations.
50 ft
Pin
50 ft
4 ft
45o 45o
All stay cables are 5 inch diameter high strength steel ropes with modulus of elasticity of 20,000 ksi.
Elevation
8 feet 6 feet 6 feet
Cross section of the bridge
Steel or Concrete box to be designed.
10” thick R/C deck slab
Guard rail
Median divider
4 feet
Centerline of Sym.
Stay cables connected to box
UNIVERSITY OF CALIFORNIA AT BERKELEY Department of Civil and Environmental EngineeringFALL SEMESTER 2008 Structural Engineering, Mechanics and Materials
Name:
Ph.D. PRELIMINARY EXAMINATION:
DESIGN
Problem 1
Consider an 18-story office building with a square hollow core, as shown. The floor beams aresimply supported at the core and suspended from the cables. The two cables are continuous overthe special saddle at the top of the building.
The service-level loads on this building are:
• Floor dead load (includes slab and beam self-weight) wD = 50 psf.
• Facade dead load wDf = 20 psf.
• Saddle dead load (equally distributed over the roof area) wDs = 150 psf.
• Typical floor live load wL = 80 psf.
• Wind load (uniform along height) wW = 25 psf.
Neglect the dead and live loads on the floor area inside the core of the building. Assume the windload acts only on the rectangular office-space facade; neglect the wind load pressure on the coreand the cables. Consider the following load combinations:
1.4D1.2D + 1.6L
1.2D + 1.6L+ 0.8W1.2D + 0.8L+ 1.6W
Use A992 steel shapes, A572 Gr. 50 plate, HSS 46 ksi tube, f ′c = 6 ksi concrete, GR60 rein-forcement, and Grade 270 post-tensioning cables with a minimum ultimate tensile strength of 270ksi. You can use other materials, but you have to specify their material characteristics.
1. (40) Design the 30x30’ core cross-section at the plaza level for the combined axial force andfirst-order bending moment it carries using the LRFD approach. Neglect P −∆ effects. Keepthe cross section square and symmetric. Investigate N-S and E-W directions to select thecritical loading, but do not consider biaxial bending.
Choose either the reinforced concrete or the steel option.
• For the R/C section, determine the thickness of the section t and the amount of rein-forcement As on one side of the section, assuming this much reinforcement will be placedon all four sides. Do not consider buckling of the core or of the reinforcement. Providea sketch of your design including reinforcing bar size and spacing.
• For the steel section, determine the thickness of the section t assuming the criticalbuckling stress is equal to 0.6Fy and that the section is compact and does not undergolateral-torsional buckling such that it can develop its full plastic moment capacity. Usethe following interaction equation:
Pu
φPn+
89Mu
φMn(1)
Provide a sketch of your design including stiffener shape and spacing needed to keep thecore cross-section wall compact.
2. (5) Conceptually design the floor system for a typical floor of this building. The reinforcedconcrete floor slab is 6 inches thick. Provide a sketch showing the joists, beams and girdersof this system.
3. (30) Design a typical floor beam B-B for the floor and facade loads it carries using the LRFDapproach. The reinforced concrete floor slab is 6 inches thick. The depth of the cross sectionbelow the slab is limited to 24 inches, such that the total beam plus slab depth is limited to30 inches. Floor deflection is limited to L/240. Choose either the reinforced concrete or thesteel option.
• For the R/C section, specify the cross section shape, dimensions and determine theamount of reinforcement. State your assumptions regarding the connection between theslab and the beam. Provide a sketch of your design including reinforcing bar size andspacing, and hoop size and spacing.
• For the steel section, use the attached table of W24 sections. State your assumptionsregarding the connection between the slab and the beam. Provide a sketch of your designincluding stud size and spacing, if they are used in design.
4. (10) Design the cable cross-section assuming it is made 0.5”-diameter GR270 post-tensioningsteel strands for the maximum tensile load it carries using the LRFD approach with φ = 0.6.
5. (15) Determine the service-load vertical downward deflection of the cable at point A and atpoint C. Assume the cable has an elastic modulus E = 23000 ksi and that it has a constantcross section throughout. Neglect the axial deformation of the roof girder A-A. Use a rationalmethod to take into account the change of force in the cable along its length between A andC. What portion of this elongation is due to the dead load?
Determine the vertical downward deflection of the cable at points A and C due to a 50oFtemperature increase in the cable. The coefficient of thermal expansion α = 6.5× 10−6 in/inper oF.
Describe how to counteract the effect of these deflections on the inclination of floor beamsduring and/or after construction?
30'
30'
18@
15'=
270'
30' 30'30'
A A
BB
cable
core
saddle
cable
floor girder
typical floor
CC
plaza
cabl
e30
'
30'
30'
As
30'
30'
t
t
N
R/C
Steel
BB
roof
University of California, Berkeley Name:________________________ Department of Civil and Environmental Engineering Structural Engineering , Mechanics and Materials
PRELIMINARY EXAMINATIONS- SPRING 2008
DESIGN Question Consider ONLY one of the two steel or reinforced concrete structures shown below. All members have the same cross section which is shown in the figures. The loads shown are service (un-factored) gravity loads P and un-factored seismic load E. Check all failure modes and calculate the seismic load E that can be applied to this structure. Concrete cover over the rebars is 2”. The steel beam is sufficiently braced and lateral-torsional buckling is not a consideration. All the information you need for this problem are given below, still, if you feel you need a piece of information that is not given, make a reasonable assumption and continue the problem. No questions can be asked during the exam. You can use approximate equations if you do not remember exact equation, but, you have to explain the approximation and how that approximation might affect your answer.
20” x 30” R/C Beam
# 4 ties @ 8”c/c
8 # 10 rebars (diameter=1.25’)
STEEL CONCRETEor
PL 1” x 12” (Top and Bott.)
y
y
PL 1”x 20”
Continuous welds at the corners
x x
Steel : Fy=36 ksi, Fu=58ksi y
y
x x
Steel rebars : Fy=60 ksi, Concrete: f’c=6,000 psi
13 ft
20 ft
E (Seismic)
30 kips (service gravity)
10 ft 13 ft
13 ft
20 ft
E (Seismic)
10 kips (service gravity)
10 ft 13 ft
