the problems in this guide are from past exams, 2011 to … fall 2017 exam 3 – past exam problems,...

CE311 Fall 2017 Exam 3 – Past Exam Problems, 2010 to 2016

1

CE 311 Exam 3 – Past Exam Problems, 2011 to 2016

Exam 3 (14% of the grade) THURSDAY, 11/16 7 TO 9:30PM. OPTIONAL Q&A SESSION WED. 11/15 7PM. Past exam problems will be posted on the website. PRIMARY COVERAGE: LESSONS 22 TO 31

Students will still need to know and apply basic material from Lessons 1 to 21 Exam is designed for 2 hours, but a maximum of 2.5 hours will be allowed

The problems in this guide are from past exams, 2011 to 2016. All problems have complete solutions given. You are allowed to have the AISC manual, a calculator, and a lucky rabbit’s foot.


2

1. (4 points) TRUE or FALSE. An A992 (Fy=50 ksi) W12x87 shape is non-compact for bending.

2. (12 points). Using ASD, what is the maximum bending moment that the center-point-loaded A992 W8x58 beam is safely allowed to carry? Given: Braced at the end-points, only.

3. (4 points) TRUE or FALSE. An A992 (Fy=50 ksi) W18x76 shape that has its compression flange laterally braced every 12

feet will reach the fully plastic moment, if loaded to failure with constant moment. 4. (12 points) Using ASD, determine the maximum uniformly-distributed-load w that the A992 W8x58 beam may safely carry,

considering the allowable bending moment. Report your answer in units of lbs/ft. Given: Span is 25-feet, simply-supported. The beam supports a concrete slab, cast on metal decking, welded to the top flange of the beam.

5. (5 points) What is the ASD allowable bending moment for an A992 (Fy=50 ksi) W24x84 shape that has its compression

flange continuously braced against lateral movement?

6. (12 points) Using ASD, determine the maximum allowable strong-axis bending moment for a W21x44 beam that has been made out of a new high-strength steel with Fy=75ksi and Fu=100ksi, for the uniformly-loaded situation shown below Given: Span is 25-feet, simply-supported. The beam supports a concrete slab, cast on metal decking, welded to the top flange of the beam.

8 feet

Brace Brace

8 feet

P

Concrete Slab

Max Safe Uniform Load w =?

Span = 25 feet

Concrete Slab

Span = 25 feet

W21 x 44


3

1. (18 points) Marooned on an island, you are planning to use an aluminum I-beam (E=10000 ksi, G=3750 ksi, Fy=40 ksi) from

your plane’s wreckage to hoist pineapples at two locations on the beam, as shown. Determine the maximum load P that the beam can resist (each bundle of pineapples will weigh P/2).

Given: Idealize and simplify the Lateral-Torsional Buckling problem by considering the beam to either be purely elastic or fully plastic, while disregarding warp torsional effects.

Bracing of the compression side is at the ends and at the load points Aluminum I-beam (E=10000 ksi, G=3750 ksi, Fy=40 ksi), consisting of 2”x¼” flange plates and a

6” x ¼” web plate. 18-foot simple span, with loads at one-third points Assume self-weight is negligible The section is compact No safety factor! You want to know the actual maximum load.

2. (2 points) TRUE or FALSE. A non-compact beam that has its compression flange continuously laterally supported by a

concrete slab would reach its fully plastic moment Mp, if loaded to failure.

3. (7 points) An A36 C9x20 shape is bent about its weak axis by a uniformly distributed load over a simple span of 5 feet. It is laterally-braced at its ends, only. Using ASD, determine the maximum uniformly-distributed load that may be safely applied (units: kips/ft).

4. (14 points) An A992 (Fy=50 ksi) W18x35 is subjected to a center-point load P over a span of 10 feet until actual failure

occurs (i.e., no safety factor – determine the actual failure load) due to strong-axis bending moment. If the beam is laterally braced at its ends, only, determine the failure load P per AISC and the failure mode (plastic, LTB, or LB). Ignore self-weight because its effect is negligible.

Brace

6’ 6’ 6’

Brace Brace Brace

P/2 P/2 Cross Section

Aluminum Beam

2” x ¼” Flange

2” x ¼” Flange

6” x ¼” Web

Brace

5 feet

Brace

Cross Section C9x20

Maximum safe distributed load w, per ASD?

C9x20

Cross Section W18x35

Brace

5’

Brace

P

5’

W18x35


4

5. (5 points) A W21x48 shape is non-compact for Fy=50 ksi. Determine its ASD allowable strength Mn/ in strong-axis bending, considering the local buckling failure mode.

6. (5 points) A beam is subjected to constant strong-axis moment. It has lateral braces spaced every 5 feet. It has the following properties: Fy= 50 ksi Zx = 50 in3 Zy = 9 in3 Sx = 40 in3 Sy = 6 in3 Lp = 3 feet Lr = 10 feet Assume residual stresses are 30% of Fy (as is standard in AISC) The section is compact

Circle the correct answer: A). Mn = 2500 kip-in

B). Mn = 1400 kip-in

C). Mn < 1400 kip-in

D). 1400 kip-in < Mn < 2500 kip-in

E). Mn > 2500 kip-in

F). Cannot be determined


5

1. (15 points) Use the ASD method to select the lightest possible A992 W section for a typical interior girder, assuring that it is

adequate for moment and deflection (live load deflection not to exceed L/360). All beams support a 3” thick slab, cast on metal deck that is welded to the top flanges of the beams. All connections are simple.

Loads: Slab: Normal Weight Concrete (150 pcf) Fill beams weigh 30 plf Live Load = 100 psf (no live load reduction shall be applied. Use 100 psf)

Do not worry about shear, as it clearly will not control

48’

50’

Plan View – Framing Plan

A B C D

1

2

3

4

35’

35’

48’ 48’


6

1. (22 points) Determine the maximum axial compression P that may be safely applied per ASD to the A992 W18x35 shape Second order effects: assume that the second order moment magnifier B1 is 1.05.

Given: The 10’-long A992 W18x35 shape is simply supported with lateral bracing at the supports, only. It is subjected to strong-axis bending due to a uniformly distributed load w=2 kip/ft, which already includes self-weight. It is also subjected to axial compression, P.

Engineering Bonus Question (4 points): Determine the net area of the C6x13 channel, considering fracture path abcd, only. Given: 5/8” bolts in standard holes.

1. (12 points) Determine the maximum normal stress due to bending* on a typical interior fill beam for the floor plan shown.

Given: W18x40 A992 fill beams in strong-axis bending. The beams support a 6” thick normal weight concrete (unit weight = 150 lb/ft3) slab, which continuously braces the top flanges of the beams, laterally.

Loads to Consider: Slab Weight, Beam Self-Weight, and a live load of 70 psf (use 70psf live load. The live load reduction factor has already been applied). Notes: All connections are simple, non-moment-resisting.

* do not consider the effect of residual stresses, as these are not “due to bending”

w = 2 kip/ft

P P

Brace

W18x35

10 - feet

Brace

36’, typ

32’, typ FLOOR PLAN


7

2. (10 points). Determine the maximum center-point load P that may be safely applied to the beam per AISC ASD Specifications,

considering bending moment limit states, only (do not consider shear or deflection limit states). GIVEN: W10x45 A992 shape (Fy=50ksi) in weak-axis bending Compression side of the beam is braced against lateral movement at the ends and at the point load Ignore self-weight (it is relatively small).

3. (12 points). Determine the maximum force P (the force that causes failure) that can be applied to the end of the 7’-long

Aluminum cantilever beam (E=10000ksi, G=3750ksi, Fy=40ksi). Because the beam is made of aluminum, LTB certainly cannot be analyzed using AISC specifications. Instead, you will treat the LTB problem by ignoring warp-torsional effects and residual stresses, while assuming that failure is either fully plastic bending or elastic buckling. Note: Cb=1 for all cantilevers. Assume self-weight is negligible.

4. (4 points). The steel beam shown has residual stresses from manufacturing equal to 0.3Fy. Fy = 50 ksi. If the beam is subjected to

x-axis positive bending moment (compression on the top and tension on the bottom) M=0.7FySx, then (circle the correct answer):

A). Actual Stress* at A is 50 ksi (compression), Actual Stress* at B is 50 ksi (tension) B). Actual Stress* at A is 35 ksi (compression), Actual Stress* at B is 35 ksi (tension) C). Actual Stress* at A is 50 ksi (compression), Actual Stress* at B is 20 ksi (tension) D). Actual Stress* at A is 20 ksi (compression), Actual Stress* at B is 50 ksi (tension) E). Actual Stress* at A is 50 ksi (compression), Actual Stress* at B is 65 ksi (tension) * Actual Stress is the stress considering the residual stress and the applied stress.

4 feet

Brace Brace

4 feet

P

Brace

W10x45 A992

7 feet

P

10”

½”

SIDE VIEW CROSS SECTION

VIEW

ALUMINUM BEAM

B

x x

A


8

5. (12 points). Using AISC ASD, determine the maximum equal-end-moments M that can be safely applied for the A992 W8x58.

Assume that the beam self-weight is negligible. Given: Braced at the end-points, only.

1. (2 points). Which shape is more efficient (e.g., can sustain a greater moment) for a strong-axis bending application if it is known that buckling modes cannot occur? Assume the cross-sectional areas are the same.

2. (5 points) True or False. An A36 S15x42.9 shape that is subjected to strong-axis bending with constant bending moment will

fail in fully-plastic bending, rather than lateral-torsional buckling if its unbraced length is 4.5 feet. 3. (2 points) True or False. A compact section is one whose flanges and webs are sufficiently thick so that the shape is able to

reach My (when LTB is prevented by continuous bracing). 4. (2 points) True or False. If the slenderness of the flange exceeds the cutoff of r, then the section will fail by local buckling

at a moment that is less than Mr, assuming that the web is compact and that LTB is prevented by continuous bracing. 5. (7 points). Evaluate the compactness of the flanges for the rolled I-shape if Fy = 50 ksi: compact, non-compact, or slender?

6. (8 points) An A36 C12x30 shape is bent about its weak axis by a uniformly distributed load over a simple span of 5 feet. It is

laterally-braced at its ends, only. Using ASD, determine the maximum uniformly-distributed load that may be safely applied (units: kips/ft).

7. (25 points). Using AISC ASD, determine the maximum constant end-moment M that can be safely applied for the shape

shown and clearly state whether it is controlled by fully plastic bending or LTB. Assume: That the beam self-weight is negligible That the residual stress is equal to 0.3Fy (per AISC Standard) Given: Braced at the end-points, only. Fy = 50 ksi. The section is compact. Flanges are 10”x5/8”. Web is 12”x3/8”.

16 feet

Brace Brace

M M

W8x58 A992

(A) (B)

14”

1/4”

12”

1/2”

Brace

5 feet

Brace

Cross Section C12x30

Maximum safe distributed load w, per ASD?

C12x30


9

Lr = 27.0 feet Ix = 553 in4, Iy = 104 in4, A = 19.5 in2

1. (2 points) TRUE or FALSE. Lateral-torsional buckling is prevented at all locations along the continuous I-shaped beam below due to the presence of the slab.

2. (12 points) The rolled shape shown was loaded with a uniform load w until it actually failed in bending. Assuming this failure is perfectly predicted by AISC specifications, determine the uniform loading w that caused this failure.

Given: Fy = 50 ksi Web is compact Flange p = 9.15 Flange r = 24.1

Ix = 6730 in4 Iy = 1167 in4 Lp = 19.3 ft. Lr = 54.7 ft

Brace Brace

M

16 feet

12”

10”

3/8”

5/8”

Concrete Slab

Uniform Load

Concrete Slab

30’

Uniform Load w 24.1”

30”½”

½”

Cross Section


10

3. (20 points). Determine the maximum safe centerpoint load P that may be applied per ASD AISC specifications.

Given: Built-up (welded) section Fy = 50 ksi 1”x12” flanges ½”x19” web Braces at the supports and at midspan Ignore self-weight (negligible) Lr = 32.8 ft Do not consider shear or deflection

4. (16 points) Determine the maximum normal stress acting within the beam, due to bending. Given:

W21 x48 (Fy = 50 ksi) beam in strong-axis bending. Distributed load w =1 kip/ft, including the self-weight Lp = 6.09’, Lr = 16.5’ There is a concrete slab on top of the beam A is a fixed support, B is a shear connection, C is a roller support. Supports are assumed to act as braces

Brace Brace

8 feet

19”

12”

½”

1”

P

Brace

8 feet

BUILT-UP SHAPE CROSS-SECTION 1” x 12” Flanges ½” x 19” Web

8 feet 6 feet

Shear Connection

w = 1 kip/ft (incudes self-weight)

A 2

B2

C2

S L A B


11

1. (2 points). Which shape is more efficient (e.g., can sustain a greater moment) for a strong-axis bending application if it is known that buckling modes cannot occur? Assume the cross-sectional areas are the same.

2. (2 points) TRUE or FALSE. If a rolled shape is known to be compact for Fy = 50 ksi then it is definitely compact for Fy = 70

ksi. 3. (2 points). TRUE or FALSE. For the flanges of W shapes, p and r are the same, whether for strong or weak-axis bending. 4. (2 points). TRUE or FALSE. A non-compact beam that has its compression flange continuously laterally supported by a

concrete slab would reach its fully plastic moment Mp, if loaded to failure. 5. (5 points) TRUE or FALSE. If loaded to failure, the A36 S15x42.9 shape will fail in fully plastic bending. Note: the section

is compact.

6. (3 points). The steel beam shown has residual stresses from manufacturing equal to 0.3Fy. Fy = 50 ksi. If the beam is

subjected to x-axis positive bending moment (compression on the top and tension on the bottom) of magnitude M=0.7FySx, then determine which of the following is true:

7. (12 points). Determine the maximum safe centerpoint load P that may be safely applied to the W16x26 A992 beam per ASD

AISC specifications. Given: Braces at the supports and at midspan Ignore self-weight (negligible) Do not consider shear or deflection Section is compact

(A) (B)

Brace Brace

4 feet

P

Brace

4 feet

A36 S15x42.9

B

x x

A). Actual Stress* at A is 50 ksi (compression), Actual Stress* at B is 50 ksi (tension) B). Actual Stress* at A is 35 ksi (compression), Actual Stress* at B is 35 ksi (tension) C). Actual Stress* at A is 50 ksi (compression), Actual Stress* at B is 20 ksi (tension) D). Actual Stress* at A is 20 ksi (compression), Actual Stress* at B is 50 ksi (tension) E). Actual Stress* at A is 50 ksi (compression), Actual Stress* at B is 65 ksi (tension) * Actual Stress is the stress considering the residual stress and the applied stress.

Brace Brace

8 feet

P

Brace

8 feet

W16 x 26 A992

A


12

8. (8 points). Determine the maximum safe centerpoint load P that may be safely applied to the W16x57 A913 Gr.70 beam per ASD AISC specifications.

Given: Ignore self-weight (negligible) Weak axis bending A913 Gr. 70 Steel: Fy = 70 ksi Do not consider shear or deflection

9. (16 points) Determine the maximum safe uniform load w that may be applied per AISC ASD specifications.

Given: Fy = 50 ksi Web is compact Flange p = 9.15 Flange r = 24.1

Ix = 8755 in4 Iy = 1774 in4 Lp = 19.7 ft. Lr = 54.1 ft

8 feet

P

8 feet

W16 x 57 A913 GR. 70

Concrete Slab

30’

Uniform Load w 22”

26”½”

1”

Cross Section


13

1. (8 points) The beam shown is an A992 W21x55 beam in strong-axis bending, with a uniform w as shown. Use ASD

specifications to determine the maximum safe load w that may be applied if the beam is 6 feet long with braces at the ends, only. Assume that deflection is not a consideration.

2. (12 points) Given: simple braced 2-bay frame (i.e., non-moment-resisting beam-column connections). The beams are subjected to a uniformly distributed dead load wD = 1 klf (this includes the beam self-weight) and a live load wL = 1 klf. The simple beam-column connections are made such that the horizontal distance from the bolts to the centerline of the column is 7”, as shown.

Circle all of the correct answers:

a. Using ASD, Column AB is subjected to P = 30 kips (compression) and M = 210 kip-in in strong axis bending where the bending causes compression on the righthand side of the member.

b. Using ASD, Column CD is subjected to P = 30 kips (compression) and M = 0 kip-in. c. Using ASD, Column AB is subjected to P = 30 kips (compression) and M = 210 kip-in in strong axis bending where

the bending causes compression on the righthand side of the member. d. Using ASD, Beam BC is subjected to M = 210 kip-in in strong-axis bending where the bending causes compression

on the top of the beam. e. KLx for member AB cannot be determined from the given information. f. KLx for member EF is 32 feet g. If column AB is compact, than it is known that the controlling limit state for bending is lateral-torsional buckling.

With Lb equal to 15 feet. h. Column EF is considered unbraced.

6 feet

w = ?? (kips / ft)

A

B C

D

wD = 1 kip / ft wL = 1 kip / ft

E

F

30 feet 30 feet

16 feet

7 in. 7 in. 7 in. 7 in.

wD = 1 kip / ft wL = 1 kip / ft


14

3. (12 points). Use ASD specifications to select an A36 solid round member to be used as a brace between column lines 2 and 3, along column line A. Specify minimum rod diameter that is needed, then round up to the nearest 1/8”.

Given: The exterior walls consist of metal studs that span vertically between the foundation and the roof, which acts as a diaphragm. All connections between steel framing are considered simple pins. The bracing is assumed to be tension-only braces (hence, they are redundant).

Wind is blowing from East to West. The code-specified Ultimate Wind pressure is 33.3psf, but because the ASD factor on wind is 0.6, this means that the ASD design wind pressure is 20 psf.

1

2

3

4

A

B

C

D

40’

35’

40’

30’

22’

30’

18’

North


15

4. (18 points) Determine the maximum axial compression P that may be safely applied per ASD to the A992 W10x45 shape Second order effects: assume that the second order moment magnifier B1 is 1.05.

Given: The 30’-long A992 W10x45 shape is simply supported with continuous bracing along the length that prevents lateral movement (i.e., in and out of the page). It is subjected to strong-axis bending due to a uniformly distributed load w=1 kip/ft, which already includes self-weight. It is also subjected to axial compression.

1. (2 points). Circle the correct answer, referring to the beam below, subjected to a uniformly-distributed load and an axial force that is tensile.

a. 2nd order effects lead to moment that is greater than the 1st order moment. b. 2nd order effects lead to moment that is less than the 1st order moment. c. The axial force has no effect on 2nd order moments. d. I’m hungry.

2. (2 points). Explain why live-load deflection is normally the design criterion, rather than total load deflection.

3. (22 points) Determine the maximum axial compression P that may be safely applied per ASD to the A992 W18x35 shape

Second order effects: assume that the second order moment magnifier B1 is 1. Given: The 10’-long A992 W18x35 shape is simply supported with lateral bracing at the supports, only. It is subjected to strong-axis bending due to a uniformly distributed load w=2 kip/ft, which already includes self-weight. It is also subjected to axial compression, P.

w = 1 kip/ft

P P Continuous lateral bracing W10x45

30 - feet

20 feet

Tensile Force

w=distributed load

Tensile Force

w = 2 kip/ft

P P

Brace

W18x35

10 - feet

Brace


16

1. (32 points)The top chord of the roof truss shown is composed of A992 W10x33 members, in strong-axis bending. Bracing

prevents lateral movement of all truss joints, as shown. All connections are pins. The top chord is loaded with point loads, as shown. Assume that self-weight is negligible. Assume that second-order effects are negligible. Determine if the W10x33 is adequate per ASD for the worst location and report all of the requested values.

2. (18 points). Use the ASD method to select the lightest possible A992 W section simply-supported beam shown, considering shear, moment, and deflection (live load deflection not to exceed L/360), as well as self-weight and report all requested values. The distributed live load is 1.2 kip/ft. The distributed dead load is 0.8 kip/ft, but does not include self-weight.

15’

10’ 10’ 10’ 10’ 10’ 10’ 10’ 10’

10kips 10kips 10kips 10kips 10kips 10kips 10kips 10kips 10kips

X X X X X

XXXX X

Legend: X = Lateral Brace

wLive = 1.2 kip/ft, wDead = 0.8 kip/ft

39 - feet

X X X X X X X X X X X X X X X X X X X X X X X X X X X X

Legend: X = Lateral Brace

Answers: Max. Applied Axial to Top Chord, P = _________ kips Allowable Compression, Pn/ = _________ kips Max. Applied Moment to Top Chord, M = ________ ft-kips Allowable Moment, Mn/ = _________ ft-kips Interaction Value: _______________ Safe or Unsafe, per ASD?

Answers:

Member Selected: __________________________ Applied Moment (incl. S.W.) ________________ft-kips Allowable Moment Mn/ __________________ft-kips Applied Shear (incl. S.W.) __________________kips Allowable Shear Vn/ _____________________kips Live Load Deflection __________________inches


17

Bonus Questions (0.1 points) 1. TRUE or FALSE. ISIS has been capturing and executing Shiite Muslims. 2. The Battle of Midway is considered the turning point in the US war against Japan in World War Two’s

Pacific theater. In what year did this battle take place? 3. What right was guaranteed by the 19th Amendment to the US Constitution? 4. Who is the only college football player to have been awarded the Heisman Trophy twice? 5. Who will win the 2015 Heisman Trophy? 6. The current Vegas line for Army-Navy is Navy -23. Who you got? 7. On what date did Mao Zedong declare the formation of The People’s Republic of China? 8. What frightening head of state recently stated, “Hopefully, no nukes will be needed” (against ISIS)? 9. TRUE or FALSE. Lafayette College shared the College Football National Championship with Alabama

in 1926.


18

1. (3 points). The problem below consists of a simply-supported, uniformly-loaded beam in strong-axis

bending that has continuous lateral support of the compression flange, while also subjected to an axial force. Circle the correct answer.

1. KLx = 20’, KLy = 20’, Lb = 20’

2. KLx = 20’, KLy = 0’, Lb = 20’

3. KLx = 20’, KLy = 0’, Lb = 0’

4. KLx = 0’, KLy = 20’, Lb = 20’

5. KLx = 0’, KLy = 20’, Lb = 0’

Uniformly Distributed Load, w

20 feet


Legend: X = Lateral BraceP P


19

2. (3 points). For which condition (A, B, or C) can a greater axial force P be safely applied, per ASD?

Cannot be determined from the given information

C 3. (3 points). Situation: You must accommodate a round hole for mechanical piping through one of the

beams that you’ve designed. Which is the preferred location for the hole (circle A or B)?

4. (3 points). Determine Vn for an A992 W16x26 beam in strong-axis bending.

5. (12 points). If the beam shown must be selected per ASD, for what moment M, unbraced length Lb, and

Cb factor would it be designed for? Given: the concrete slab was cast on metal decking that was welded to the top flange of the beam. The uniform loading of w = 1 kip/ft includes the beam self-weight and all other loads.


20 feet


Legend: X = Lateral BracePP

A


20 feet


Legend: X = Lateral BracePP

B

w w

Hole Hole

B A

Concrete Slab

Uniform Load w = 1 kip/ft

12’ 8’


20

6. (27 points). Determine if member AB is safe per ASD but do not consider shear or deflection. Given: A is a pinned support. B is pinned connection. Position B contains a brace that prevents lateral movement (in or out of the page). C is a pinned support. Member AB is an A992 W16x36 shape, oriented as shown. The distributed loading on AB includes the self-weight of AB. Assume that the B1 multiplier for second-order effects is 1.05.

1. (10 points). The typical interior fill beams shown are A992 W21x44. If they support a 5” thick concrete slab that provides continuous lateral support, determine the maximum live load pressure (psf) that may be applied to these beams, while satisfying ASD. Loads consist of dead and live, only. Dead loads consist of the slab and the beam self-weight. Assume that deflection is not a consideration.

2. (25 points). Determine the PM interaction ratio per ASD. Do not consider shear or deflection.

Given: A is a pinned support. B is pinned connection. Position B contains a brace that prevents lateral movement (in or out of the page). C is a pinned support. Member AB is an A992 W16x36 shape in strong-axis bending. It supports a concrete slab, cast on metal decking that is welded to the top flange of the beam. The distributed loading on AB includes the self-weight of AB. Assume that the B1 multiplier for second-order effects 1.00.

w = 2 kip/ft (incl S.W.)

A B

C 10 feet

12 feet

5 feet

XBrace

40’, typ.

40’, typ.

Plan View – Framing Plan

A B C D

1

2

3

4


21

1. (5 points). Determine the LRFD design strength Rn for the welds, considering base metal and weld metal. The base metals are

A36. The E60 fillet welds are 3/8”. The gusset is ¼” thick. The angles are 2L5x5x½”

w = 2 kip/ft (incl S.W.)

A B

C 10 feet

12 feet

5 feet

XBrace

Concrete Slab

W16x36

Cross-Section 2L5x5x½” ¼” Gusset

3/8” E60 Welds

Rn

3/8” – 10”

3/8” – 5”

the problems in this guide are from past exams, 2011 to … fall 2017 exam 3 – past exam problems,...

Documents