+ All Categories
Home > Documents > 3.00 credit, 3hrs/week -

3.00 credit, 3hrs/week -

Date post: 31-Oct-2021
Category:
Upload: others
View: 2 times
Download: 0 times
Share this document with a friend
112
CE 317: Design of Concrete Structures II 3.00 credit, 3hrs/week Dr. Tahsin Reza Hossain Professor, Room No-536 Email: [email protected] Web: trhossain.info 1
Transcript

CE 317: Design of Concrete Structures II 3.00 credit, 3hrs/week

Dr. Tahsin Reza Hossain Professor, Room No-536

Email: [email protected]

Web: trhossain.info

1

Syllabus • Design of column supported slabs • Introduction to floor systems • Design of columns under uniaxial and biaxial

loading, Introduction to slender column • Structural design of footings, pile caps • Seismic detailing • Shear wall • Structural forms • Introduction of prestressed concrete, Analysis

and preliminary design of prestressed beam section

New

2

Class routine

• A section- Tuesday (3)

• B section- Tuesday (1)

• C section- Sunday (2)

3

Books

• Design of Concrete Structures

– Nilson, Darwin, Dolan 15th Ed

• Structural Concrete- Theory and Design

– Hassoun, Al-Manaseer 4th Ed

• Reinforced Concrete- Mechanics & Design

– Wight & McGregor 5th Ed

Many more……..

4

COLUMNS

Short columns Chapter 8

5

• Columns are members that carry loads chiefly in compression

• Usually also carry bending moment. Tensile stresses may be produced over a part of the cross section

• Columns are generally referred to as compression member. Compression dominates behavior

Introduction: Axial Compression

6

• Generally vertical members

• Also arches, truss members,

• Column= compression member

7

Gravity load Lateral load

8

Three types of column

1. Members reinforced with longitudinal bars and lateral ties

2. Members reinforced with longitudinal bars and continuous spirals

3. Composite compression members

• 1 and 2 are common

9

Types- 1. Tied Column

10

2. Spirally reinforced column

11

12

3. Composite columns

13

Main reinforcement • Main reinforcement is longitudinal, parallel to

load, square, rectangular or circular arrangement

• Reinf ratio- 0.01 to 0.08 (1 to 8 %)

• Lower limit to ensure resistance to bending not accounted for and reduce effects of creep and shrinkage

• Higher limit – not economical and difficult due to congestion

• Normally 2-3 %, preferably not exceed 4%.

14

Main reinforcement

• Higher size (No 5 and more) used

• Even No 14 and No 18, even bundled

• Minimum 4 longitudinal bars when rectangular or circular ties

• Minimum 6 bars when continuous spiral is used

15

Short column and Slender column

• Secondary effects - buckling

16

Reinforcements –usual sizes

• Slab- No 3, 4, 5 (10mm, 12mm, 16mm)

• Beam- No 5,6, 7, 8 (16 20 22 25mm)

• Stirrup/tie- No, 3 4 (10 12mm)

• Column –No 5, 6 7 8 9 10 11 14 18 (16 20 22 25 28 32 ….)

• Mat- No 4,5,6,8 (12 16 20 25 mm)

• Smaller sizes preferred as long as there is no congestion

17

18

19

20

NominalStrength

Elastic range

21

Design strength

22

23

8.2 Lateral ties and spiral

24

• Large P, small M – longitudinal bars uniform (a to d)

• Large M – bars at maximum distance from axis of bending

• Bundled bar- 2,3,4

• Bundled bars act as a unit

25

Purpose of Lateral ties and spiral

• Hold longitudinal bar in position while concrete is placed

• Prevent longitudinal bars from buckling

• Shear steel

26

ACI provisions for ties

27

ACI provisions for spirals

28

• 𝑃𝑢 ≤ 𝛼∅𝑃𝑛 Demand< Capacity

• 𝑃𝑛 = 0.85𝑓𝑐′ 𝐴𝑔 − 𝐴𝑠𝑡 +𝐴𝑠𝑡𝑓𝑦

29

Axially loaded column

30

• 𝛼 = 𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡𝑎𝑙 𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦

=0.80 for tied column

=0.85 for spiral column

• ∅ = 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟

=0.65 for tied column

=0.75 for spiral column

31

Purpose of Lateral ties and spiral

• Hold longitudinal bar in position while concrete is placed

• Prevent longitudinal bars from buckling

• Shear steel

• Spiral gives confinement

• All bars shall be enclosed by lateral tie

• #3 tie bar for up to longitudinal bar #10

• #4 tie bar for longitudinal bar #11 and above

• #4 tie bar for bundled longitudinal bar

• Spacing of tie shall be less than

– 16dlong, 48dtie, Least dim

32

ACI provisions for ties

• Every corner and alternate bar shall have lateral support provided by corner of tie (<135)

• Clear spacing between supported bar and unsupported bar shall be less than 6in.

33

ACI provisions for ties

34

35

Problem 1

• Determine nominal and design axial compression capacity of a column 12˝X12˝reinforced with 4 No 9 bars. Also check the ties No. 3 @ 12in c/c. Given: fc’= 4ksi and fy=60 ksi.

36

37

Problem 2

• Design a tied column for

– PDL= 300 kip and PLL= 200 kip

– fc’= 3 ksi and fy=60 ksi

38

39

40

41

42

Problem 3

• Design a tied column with section 10˝x10˝ for

– PDL= 60 kip and PLL= 30 kip

– fc’= 3 ksi and fy=60 ksi

43

44

Problem 4. • Determine nominal and design axial

compression capacity of a circular pile 40inch diameter reinforced with 40 No. 10 (32mm) bars. Also design the ties. Given: fc’= 3ksi and fy=60 ksi. Note bundle bars. Alternate bars?

45

46

Spirally reinforced column

• If filled with sand, load carrying capacity is due to hoop tension only

• If filled with concrete, it can carry without confinement

• Closely spaced spiral behaves like this drum, ie. it counteracts expansion of concrete

• Capacity of the core greatly increased

• Failure occurs when spiral yields and confinement greatly reduces

47

Tied and spiral behavior • A tied column fails when load reaches Pn

• Concrete fails in crushing and shearing in inclined plane

• Longitudinal steel buckles between ties

• A spirally rein column, the outer shell spalls off at the same load Pn

• Depending on the amount of spiral, the failure load can be much higher than Pn

• Axial strain will be much higher- higher toughness

48

Effect of confinement

• Increases strength

• Increases failure strain

• Ductility and toughness 49

Failure of tied and spiral columns

50

51

ACI spiral (also BNBC 2020)

• Excess capacity is wasted

• ACI provides minimum amount of spiral that contributes to capacity slightly higher than that concrete shell

• This is ACI spiral-

• It hardly increases Pn

• It prevents instantaneous crushing, buckling of long steel, produces a gradual and ductile failure- a tougher column

52

ACI spiral derivation

53

54

55

56

57

Problem 5

• Design a circular spiral column to support

– PDL= 475 kip and PLL= 250 kip

– fc’= 4 ksi and fy=60 ksi

– Steel ratio of about 3%.

– Also design necessary spiral

58

59

60

61

Compression plus Bending

Rectangular columns

62

• Columns chiefly carries compression

• But bending is almost always present

– By continuity, part of monolithic frames

– By transverse loads, wind, earthquake

– By eccentric on bracket

– By inevitable construction imperfection

– Arch axis not coincides with pressure line

63

Statically equivalent • Two loads are statically equivalent

• Columns can be classified by e

• Small e – Comp over entire section

– If overloaded, fails by crushing of concrete and yielding of steel in comp in overloaded side

• Large e – Some part in tension

– If overloaded, may fail in yielding of steel in tension at the farthest side from load

64

65

8.4 Strain Compatibility Analysis and Interaction diagram

66

67

• For large reinforcement ratio

• For large e

– Failure is initiated by yielding of tension steel fs=fy

– When εu is reached, compression steel may or may not have yielded, can be found from compatibility of strain

• For small e

– εu is reached before tension steel yields

– Stress in the other side of load may also be in compression, not in tension.

68

69

Interaction diagram

70

71

72

Balanced Failure

73

74

75

Problem

76

77

78

79

80

81

82

83

84

85

86

Read article- important 87

Why phi is low for column?

88

Why alpha?

89

DESIGN CHARTS

90

91

92

93

94

95

96

97

Review problem

• Use the charts to determine the column strength ϕPn, of the short column shown in Fig (14x24, reinforced with 8 No 10 bars), Use fc’=4ksi and fy=60 ksi, e=12in

98

99

BIAXIAL BENDING

• There are situations when axial compression is associated with simultaneous bending present about both principal axes of the section

• Corner column is such a case

• Interior column may also experience biaxial bending-irregular grid, lateral load

100

101

Load contour method

102

103

Reciprocal Load method

104

105

Example 8.5

106

107

108

109

110

111

For both axially loaded and biaxial problems, alpha phi Pn should be greater than max Pu .

Ignore Mu first, check two problems of last year

do not use graph paper for interaction, make hand sketch

don’t attach charts

End of short Column 112


Recommended