Sample fundamentals of structural analysis 5th edition Leet solution manual pdf | answer key PDF

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Authors: Kenneth M. Leet , Chia-Ming Uang , Joel T. Lanning | Anne M. Gilbert
Published: McGraw-Hill Education 2018
Edition: 5th
Pages: 654
Type: pdf
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FOLFNKHUHWRGRZQORDG

FUNDAMENTALS OF STRUCTURAL ANALYSIS 5th Edition Kenneth M. Leet, Chia-Ming Uang, Joel T. Lanning, and Anne M. Gilbert

SOLUTIONS MANUAL

CHAPTER 2: DESIGN LOADS AND STRUCTURAL FRAMING

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FOLFNKHUHWRGRZQORDG 72ʺ

P2.1. Determine the deadweight of a 1-ft-long segment of the prestressed, reinforced concrete tee-beam whose cross section is shown in Figure P2.1. Beam is constructed with lightweight concrete which weighs 120 lbs/ft3.

6ʺ 6ʺ 48ʺ

8ʺ

24ʺ 12ʺ 18ʺ Section

P2.1

Compute the weight/ft. of cross section @ 120 lb/ft3.

Compute cross sectional area: æ1 ö Area = ( 0.5 ¢´ 6 ¢) + 2 çç ´ 0.5 ¢´2.67 ¢÷÷÷+ (0.67 ¢´ 2.5 ¢)+ (1.5 ¢´1 ¢) èç 2 ø = 7.5 ft 2

Weight of member per foot length:

wt/ft = 7.5 ft 2 ´120 lb/ft 3 = 900 lb/ft.

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FOLFNKHUHWRGRZQORDG P2.2. Determine the deadweight of a 1-ft-long segment of a typical 20-in-wide unit of a roof supported on a nominal 2 × 16 in. southern pine beam (the actual dimensions are 21 in. smaller). 2 The 43 -in. plywood weighs 3 lb/ft .

2ʺ insulation

three ply felt tar and gravel

3/4ʺ plywood

151/ 2ʺ

1 1/ 2ʺ

20ʺ

20ʺ Section

P2.2

See Table 2.1 for weights wt / 20 ¢¢ unit 20¢¢ ´ 1¢ = 5 lb 12 20¢¢ ´ 1¢ = 5 lb Insulation: 3 psf´ 12 20¢¢ 9.17 lb Roof’g Tar & G: 5.5 psf ´ ´1¢ = 12 19.17 lb ¢¢ lb (1.5¢¢ ´15.5) ´1¢ = 5.97 lb Wood Joist = 37 3 ft 14.4 in 2 / ft 3 ¢¢ Total wt of 20 unit = 19.17 + 5.97 Plywood: 3 psf´

= 25.14 lb. Ans.

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FOLFNKHUHWRGRZQORDG P2.3. A wide flange steel beam shown in Figure P2.3 supports a permanent concrete masonry wall, floor slab, architectural finishes, mechanical and electrical systems. Determine the uniform dead load in kips per linear foot acting on the beam. The wall is 9.5-ft high, non-load bearing and laterally braced at the top to upper floor framing (not shown). The wall consists of 8-in. lightweight reinforced concrete masonry units with an average weight of 90 psf. The composite concrete floor slab construction spans over simply supported steel beams, with a tributary width of 10 ft, and weighs 50 psf. The estimated uniform dead load for structural steel framing, fireproofing, architectural features, floor finish, and ceiling tiles equals 24 psf, and for mechanical ducting, piping, and electrical systems equals 6 psf.

8ʺ concrete masonry partition 9.5ʹ

concrete floor slab

piping mechanical duct wide flange steel beam with fireproofing ceiling tile and suspension hangers Section

P2.3

Uniform Dead Load WDL Acting on the Wide Flange Beam:

Wall Load: 9.5¢ (0.09 ksf) = 0.855 klf Floor Slab: 10¢ (0.05 ksf) = 0.50 klf Steel Frmg, Fireproof’g, Arch’l Features, Floor Finishes, & Ceiling: 10¢ (0.024 ksf)= 0.24 klf Mech’l, Piping & Electrical Systems: 10¢ (0.006 ksf) = 0.06 klf Total WDL =1.66 klf

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FOLFNKHUHWRGRZQORDG 1

P2.4. Consider the floor plan shown in Figure P2.4. Compute the tributary areas for (a) floor beam B1, (b) floor beam B2, (c) girder G1, (d) girder G2, (e) corner column C1, and (f ) interior column C

2

3

6 @ 6.67ʹ = 40ʹ

C4

A B2

G1 B4

B3

2 @ 10ʹ = 20ʹ

C2

B

G4 G2

G3

B1

C

5 @ 8ʹ = 40ʹ

C3 40ʹ

C1 20ʹ

P2.4

(a ) Method 1: AT Method 2: AT

(b ) Method 1: AT Method 2: AT

8 8      40   A  3 20 ft 2 2 1   320  4  4(4)   A  288 ft 2   6.67   20   A  66.7 ft    2  1   66.7  2  3.33(3.33)   A  55.6 ft 2 

4 ft

36 ft

T

B1

B1

2

T

6.67 ft

6.67 ft

2

10 ft

10 ft

2

T

 6.67  20  10(10)    2 

AT  166.7 ft

Right Side

6.67 ft

2

1 2

 

36 ft

5(5)

4 ft

G2

G2

2

1 2

Metho d 2: AT  1080  2 

 

4(4 )

B4

2

A T,C2

 40   20  ; A  200 ft     2  2   40  20   40  2 0  ; A     2 2  2 2  2

T

T

A T,C1

 900 ft 2

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6.67 ft

36 ft

2

 40 20  36    2 2

AT 1096 ft

6.66 ft

4 ft

(d ) Method 1: AT  

AT 1080 ft

5 ft

G1

G1

1   3.33(3.33)   2  2  

AT  180.6 ft

5 ft

Left Side

Method 2: AT 166.7  2 

( f ) AT

6.66 ft

T

(c ) Method 1: AT  

( e ) AT 

4 ft

2

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FOLFNKHUHWRGRZQORDG 1

P2.5. Refer to Figure P2.4 for the floor plan. Calculate the tributary areas for (a) floor beam B3, (b) floor beam B4, (c) girder G3, (d) girder G4, (e) edge column C3, and (f ) corner column C4.

2

3

6 @ 6.67ʹ = 40ʹ

C4

A B2

G1 B4

B3

2 @ 10ʹ = 20ʹ

C2

B

G4 G2

G3

5 @ 8ʹ = 40ʹ

B1

C

C3 40ʹ

C1 20ʹ

P2.4 5 ft

(a ) Method 1: A T   10  20  AT  200 ft Method 2: A T

2

B3 2

6.67 ft

6.66 ft

6.67 ft

2

B4

(b ) Method 1: AT   6.67  20   AT  133.4 ft Method 2: AT

5 ft

B3

1   200  4  5  2 

AT  150 f t

10 ft

B4 36 ft

36 ft

2

4 ft

4 ft

1   133.4  4  3.33  2  2

AT 111.2 ft

G3

G3

2

33.33 ft 2 (c ) Method 1: AT   36 20  AT  720 ft

3.33 ft

Right Side

1 2  2 Method 2: AT  720  2  4   AT  736 ft 2 

Left Side

4 ft

G4

(d ) Method 1: AT   4 40  33.33(10) AT  493.4 ft

 1 4   2  1 3.33     2  2  2

2

A T,C4

B4

2

(e ) AT   30  20 ; A T  600 ft

2

( f ) AT   10 10 ; A T  100 ft

AT,C3

2

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3.33 ft

36 ft

G4

2

Method 2: AT  493.4  2  AT  488.5 ft

33.33 ft

4 ft

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FOLFNKHUHWRGRZQORDG 1

P2.6. The uniformly distributed live load on the floor plan in Figure P2.4 is 60 lb/ft 2. Establish the loading for members (a) floor beam B1, (b) floor beam B2, (c) girder G1, and (d) girder G2. Consider the live load reduction if permitted by the ASCE standard.

2

3

6 @ 6.67ʹ = 40ʹ

C4

A B2

G1

B3

B4

2 @ 10ʹ = 20ʹ

C2

B

G4 G3

G2 5 @ 8ʹ = 40ʹ

B1

C

C3

C1

40ʹ

20ʹ

P2.4

2

w

(a ) AT = 8(40) = 320 ft , K LL = 2, AT K LL = 640> 400

æ çè

÷÷ö= 50.6 psf > 60 , ok ÷ 2 640 ø

15

L = 60 çç0.25 +

B1 and B2

w = 8(50.6) = 404.8 lb/ft = 0.40 kips/ft

(b ) AT =

6.67 2

w=

(c ) A T =

6.67 2

6.67 2

w=

2 (20) = 66.7 ft , K LL = 2, AT K LL = 133.4< 400, No Reduction

(60) = 200.1 lb/ft = 0.20 kips/ft

2

(20) + 10(10) = 166.7 ft , K LL = 2, AT K LL = 333.4 < 400, No Reduction

6.67

P

(60) = 200.1 lb/ft = 0.20 kips/ft

w

2 P=

q (Wtrib )(Lbeam ) 2

=

60(10)(20) 2

= 6000 lbs = 6 kips

G1

æ 40 20ö 2 ÷ çè 2 + 2 ÷÷ø 36 = 1080 ft , K LL = 2, AT K LL = 2160 > 400 æ 15 ÷ö 60 L = 60 çç0.25 + ÷÷ = 34.4 > , ok çè 2 2160 ø

(d ) A T = çç

P

P

P

L = 34.4 psf

æ 40 20ö ÷ çè 2 + 2 ÷÷ø = 8256 lbs = 8.26 kips

P = 8(34.4)çç

5 spaces @ 8’ each

G2

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P

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FOLFNKHUHWRGRZQORDG 1

P2.7. The uniformly distributed live load on the floor plan in Figure P2.4 is 60 lb/ft 2. Establish the loading for members (a) floor beam B3, (b) floor beam B4, (c) girder G3, and girder G4. Consider the live load reduction if permitted by the ASCE standard.

2

3

6 @ 6.67ʹ = 40ʹ

C4

A B2

G1 B4

B3

2 @ 10ʹ = 20ʹ

C2

B

G4 G3

G2 5 @ 8ʹ = 40ʹ

B1

C

C3 40ʹ

C1 20ʹ

P2.4

2

(a ) AT = 10(20) = 200 ft , K LL = 2, AT K LL = 400> 400

w

æ 15 ö÷ L = 60 çç0.25 + ÷÷ = 60 psf èç 400 ø B3 and B4

w = 10(60) = 600 lb/ft = 0.60 kips/ft

2

(b ) AT = 6.67(20) = 133.4 ft , K LL = 2, AT K LL = 266.8 < 400, No Reduction w = 6.67(60) = 400.2 lb/ft = 0.40 kips/ft 2

(c ) A T = 36(20) = 720 ft , K LL = 2, AT K LL = 1440 > 400

æ çè

ö 60 ÷÷÷ = 38.7 psf > , ok 2 1440 ø

P

P

P

15

L = 60 çç0.25 + P=

P

q (Wtrib )(Lbeam ) 2

=

38.7(8)(40) 2

5 spaces @ 8’ each

= 6192 lbs = 6.19 kips

æ 8 ö÷ 2 ÷ 40 + 33.33(10) = 493.3 ft , K LL = 2,AT K LL = 986.6> 400 è 2 ÷ø æ 15 ÷ö 60 L = 60 çç0.25 + ÷÷ = 43.7 > , ok çè 2 986.6 ø

G3

(d ) A T = çç

w

P

P

P

P

w = 43.7(4) = 174.8 lb/ft = 0.17 kips/ft P =

43.7(6.67(20) 2

6 spaces @ 6.67’ each

= 2914.8 lbs = 2.91 kips

G4

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FOLFNKHUHWRGRZQORDG

3 @ 12ʹ = 36ʹ

P2.8. The building section associated with the floor plan in Figure P2.4 is shown in Figure P2.8. Assume a live load of 60 lb/ft2 on all three floors. Calculate the axial forces produced by the live load in column C1 in the third and first stories. Consider any live load reduction if permitted by the ASCE standard. C3

C1

40ʹ 20ʹ Building Section P2.8

æ 40 20öæ 40 20 ö + ÷÷çç + ÷÷ = 900 ft2 , K LL = 4, AT K LL = 3600 > 400 ÷ èç 2 øè 2 2 2 ø÷ æ 15 ÷ö 60 L = 60 çç0.25 + ÷ =30 psf = , ok (minimum permitted) çè ÷ 2 3600 ø

(a ) AT = çç

P3rd = 900(30) = 27000 lbs = 27 kips P1st = (3)900(30) = 27000 lbs = 81 kips

B4 A T,C2

A T,C1

PLAN

P3rd

P1st C2

ELEVATION

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FOLFNKHUHWRGRZQORDG

3 @ 12ʹ = 36ʹ

P2.9. The building section associated with the floor plan in Figure P2.4 is shown in Figure P2.8. Assume a live load of 60 lb/ft2 on all three floors. Calculate the axial forces produced by the live load in column C3 in the third and first stories. Consider any live load reduction if permitted by the ASCE standard. C3

C1

40ʹ 20ʹ Building Section P2.8

æ 40 20 ö÷ 2 + ÷ 20 = 600 ft , K LL = 4, AT K LL = 2400 > 400 ÷ çè 2 ø 2 æ 15 ÷ö 60 L = 60 çç0.25 + ÷÷= 33.4 psf = , ok çè 2 2400 ø

(a ) AT = çç

P3rd = 600(33.4) = 20040 lbs = 20.0 kips P1st = (3)600(33.4) = 60120 lbs = 60.1 kips

A T,C4

B4

A T,C3

PLAN

P3rd

P1st C3

ELEVATION

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FOLFNKHUHWRGRZQORDG P2.10. A five-story building is shown in Figure P2.10. Following the ASCE standard, the wind pressure along the height on the windward side has been established as shown in Figure P2.10(c). (a) Considering the windward pressure in the east-west direction, use the tributary area concept to compute the resultant wind force at each floor level. (b) Compute the horizontal base shear and the overturning moment of the building.

1

2

3

4

5

A

3 @ 30ʹ = 90ʹ

N

B

C

D 4 @ 25ʹ = 100ʹ

(b)

(c)

20 psf (6 × 90) = 10,800 lb 20 psf (12 × 90) = 21,600 lb

th

20 psf (2 × 90) + 15 (10 × 90) = 17,100 lb

rd

15 psf (10 × 90) + 13 (2 × 96) = 15,800 lb

nd

13 psf (12 × 90) = 14,040 lb

5 floor 4 floor 3 floor 2 floor

b) Horizontal Base Shear VBASE = Σ Forces at Each Level = 10.8k + 21.6k + 17.1k + 15.8k + 14.04k =

(a)

k

VBASE = 79.34

Overturning Moment of the Building = Σ (Force @ Ea. Level × Height above Base) 10.8k (60′)+ 21.6 (48′) + 17.1 (36′) + 15.8k (24′)+ 14.04k(12′) = M overturning = 2, 848ft.k

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13

wind pressures in lb/ft2

a) Resulant Wind Forces th

15

Building Section

P2.10

Roof

20

3 @ 20ʹ = 60ʹ

5 @ 12ʹ = 60ʹ

Plan ( a)

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FOLFNKHUHWRGRZQORDG P2.11. A mechanical support framing system is shown in Figure P2.11. The framing consists of steel floor grating over steel beams and entirely supported by four tension hangers that are connected to floor framing above it. It supports light machinery with an operating weight of 4000 lbs, centrally located. (a) Determine the impact factor I from the Live Load Impact Factor, Table 2.3. (b) Calculate the total live load acting on one hanger due to the machinery and uniform live load of 40 psf around the machine. (c) Calculate the total dead load acting on one hanger. The floor framing dead load is 25 psf. Ignore the weight of the hangers. Lateral bracing is located on all four edges of the mechanical floor framing for stability and transfer of lateral loads.

3ʹ

10ʹ

3ʹ hanger

hanger

2.5ʹ

vertical lateral bracing, located on 4 sides of framing (shown dashed) mechanical unit

5ʹ

hanger 2.5ʹ edge of mechanical support framing

hanger Mechanical Floor Plan (beams not shown) (a)

floor framing above supports

vertical lateral bracing beyond hanger hanger

mechanical unit

floor grating

mechanical support framing Section (b)

P2.11

a) Live Load Impact Factor = 20% b) Total LL = 4.8k

Machinery = 1.20 (4 kips)

Uniform LL = ((10′ × 16′) ‒ (5′ × 10′)) (0.04 ksf) = 4.4k Total LL = 9.2k ∴ Total′ LL Acting on One Hanger = 9.2k/4 Hangers = 2.3klps c) Total DL = 4k

Floor Framing = 10′ × 16′ (0.025 ksf)

∴ Total DL Acting on one Hanger = 4k/4 Hangers = 1 kip ∴ Total DL + LL on One Hanger = 2.3k + lk = 3.3 kips

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FOLFNKHUHWRGRZQORDG qz GCp

P2.12. The dimensions of a 9-m-high warehouse are shown in Figure P2.12. The windward and leeward wind pressure profiles in the long direction of the warehouse are also shown. Establish the wind forces based on the following information: basic wind speed = 40 m/s, wind exposure category = C, Kd = 0.85, Kzt = 1.0, G = 0.85, and Cp = 0.8 for windward wall and ‒0.2 for leeward wall. Use the Kz values listed in Table 2.4. What is the total wind force acting in the long direction of the warehouse?

Use I = 1

qhGCp

20 m