preliminary examination- design question · question 1. check the design of the steel “jib”...

Student’s Name (Please Print) ______________________________________

Structural Engineering Mechanics and Materials Department of Civil and Environmental Engineering, University of California at Berkeley

Fall 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.

Consider the elevated water tank shown in the sketch and the gravity, wind and seismic loads given below. See additional information on design and loads on the next page. Design of water tank itself and the conical skirt at the base is not part of this problem. Here are what you are required to do:

1. Design the cylindrical part of the column supporting the tank assuming it is made of hollow steel pipe with external diameter of 6 feet. You are asked to select appropriate materal and calculate the required thickness of the steel pipe considering all applicable failure modes.

2. Provide a neatly drawn sketch of the base plate –anchor rod-foundation detail at the base of the steel skirt with all elements identified on the sketch. Suggest what material will you use for each element and why? Then list all failure modes you would consider if you were given the time to check the design of the detail you provided. No calculation is needed for this part, just provide write-up.

3. Design the pipe column again but this time assume it is made of a hollow reinforced concrete pipe with external diameter of 8 feet and internal diameter of 6 feet. You are asked to select appropriate materal for concrete and steel and calculate the required longitudinal rebars and transvers ties.

26 ft

Spherical Steel Water Tank with: External Dia.=20 ft Weight of Empty Tank= 50 kips Weight of Water When Tank is Full= 260 kips

70 ft

For Steel Case: Hollow Steel Pipe with: External Dia.= 6 ft Thickness of the Pipe = To be Calculated

For Steel case you need to provide a sketch showing details of this base connection.

For Concrete Case: Hollow R/C Pipe with: External Dia.= 8 ft Internal Dia. = 6 ft Thickness of the Pipe = 1 ft

Here is additional information:

1. Moment of inertia of a pipe is given by I = π (do4 - di

4) /64 , where do and di are outside and inside diameter of the pipe respectively. Plastic section modulus of a pipe is given by Zx= (do

3 - di3) /6. Assume a constant diameter

and thickness for the steel and concrete pipe throught the 70 ft of length. For steel pipe, use the interaction equation: P/Pcr + (M/Mp)2 =1.0. In this equation, Pcr is the Euler’s buckling load equal to π2EI/(KL)2. E is the modulus of elasticity of steel equal to 29,000 ksi, I is the moment of inertia, K is the effective length factor (need to be selected by you), and L is the length of the member. Mp in the equation is plastic moment capacity equal to Zx Fy , where Zx is plastic section modulus and Fy is specified minimum yield stress of the steel. P and M are the applied factored axial load and bending moment respectively. For concrete pipe select appropriate equations and procedure to follow and explain your assumptions. Limit the horisontal displacement of the center of the tank to 0.002 times its distance from the base for seismic and to 0.001 for wind.

Loading: Seismic Load is given by Acc. Response Spectrum below. Wind load is 30 pounds/ft2 of the projected area perpendicular to the direction of the wind. Wind load does not change over the height. Consider appropriate combinations of gravity, wind, and seismic. If you do not remember exact value of the load factors, use a number that makes most sense to you.

Student’s Name (Please Print) ______________________________________

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

Name: _____________________________________________

1

University of California Department of Civil and Environmental Engineering Fall Semester 2013 Structural Engineering, Mechanics and Materials

Preliminary Examination

Structural Engineering Design

Some of the questions below are conceptual and open ended in nature. If you do not feel you have enough information to answer the question, you may make any reasonable assumption needed so long as you explain your thinking clearly. 1. Consider the seismic detailing of a weightless girder that is part of a reinforced

concrete moment resisting frame. The frame is to be designed to behave in a highly ductile manner, and may be subjected to earthquakes significantly (say 8 times) greater than it can withstand elastically. The girder is 30 feet long, and 30 inches deep.

For this problem, vertical gravity loads, and the effects of horizontal earthquake forces should be considered, but vertical earthquake effects should be ignored.

The figure to the right shows the nominal moment capacities of the girder at the ends and middle. The moments are based on nominal strengths of materials. Moments are shown on the face corresponding to yielding of the tension reinforcement on that side of the beam.

The vertical gravity load shown at the middle of the beam has already been adjusted to account for all code related load factors for combinations related to earthquake effects.

a. Conceptually describe (with sketches) the deformed shape of the member if plastic hinges form (i) only at the ends of the girder, or (ii) at other locations during lateral seismic displacement of the building?

b. Briefly describe why one might prefer to have plastic hinging only near the ends of the member.

c. For the specific beam shown, where do you expect the girder to form plastic hinges during a very large earthquake? Show calculations to justify your answer.

d. Based on these calculations, make sketches to illustrate how you would detail the member. That is, you do not need to compute specific bar sizes or dimensions, but just schematically indicate locations where you would place longitudinal reinforcement, and the basic type, location and detailing of transverse reinforcement along the girder.

Name: _____________________________________________

2

e. Compute the maximum shear force that should be considered in the design of the girder? Where does this shear occur?

[If you believe you are not familiar enough with reinforced concrete to do this problem, you may consider the same problem but considering it to be constructed in steel. For part d, identify special detailing requirements that would be needed at various points along the beam.]

2. Consider the seismic design of a column designed to support a high-speed train. To preserve post-earthquake operability, the column is expected to remain elastic. A sketch of the system is shown below. The column section must be circular. For a reinforced concrete section, the minimum total area of longitudinal steel is 1% of the gross area of the section. For hollow steel sections, the thickness of the steel must be greater than the outer diameter of the member divided by 32. For this problem, you may assume normal weight concrete with a compressive strength of 5 ksi, Grade 60 A706 reinforcing bars, or A709-50W plate (fy=50ksi) (these can be rolled and welded to make large diameter circular sections)

The earthquake spectra for design are specified by two pseudo-accelerations, one at a period of 0.2 second and the other at 1 second. The corresponding values are Ss= 1.1 in/sec2 and S1 = 0.6 in/sec2.

a. There is a requirement intended to control train vibrations under normal operations that requires the longest period of the structure not to exceed 0.3 seconds. What is the minimum size column you can use?

b. There is a requirement that the nominal stress in the column caused by the applied gravity load not exceed 0.1Agf’c for a concrete section or 0.1AsFy for a steel section. What is the minimum sized column you can use?

c. For the earthquake case, the displacement of the structure should not exceed 1 inch. What is the minimum sized column you can use?

d. Pick an acceptable section satisfying the criteria stated above. Then, compute the design moment corresponding to the earthquake response spectra specified.

e. For this bending moment, estimate the amount of longitudinal steel required for a reinforced concrete column or the thickness required for a circular steel column. Because of the low axial load, it is acceptable for this problem to ignore the effects of axial load on moment capacity. For a reinforced concrete section, simplifying assumptions, if explained, can be used to estimate the moment of a circular column

Name: _____________________________________________

3

having many distributed longitudinal reinforcing bars. Draw a sketch of your section showing the basic design features.

f. While the column is expected to remain elastic for this level of shaking, it is possible that larger earthquakes might occur. Thus, capacity design methods should be considered. Describe briefly how you would use capacity design concepts to compute other design forces and detail the column and foundation. These elements are not to be designed. Only explain how you would approach this problem, given the design of the column you have obtained in part e.

Reference: For a circular section in terms of the outer and inner RADII (Ro and Ri), the area is π(Ro2-Ri2), moment of inertia is π(Ro4-Ri4)/4, and plastic section modulus is π(Ro3-Ri3)/48.

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.


30 kips

Wind


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!

okimoto

Text Box

Name _________________________________________

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.



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.



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

okimoto

Text Box

Fall 2009

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

preliminary examination- design question · question 1. check the design of the steel “jib”...

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