Beam design

Design in reinforced concrete

Prepared by: M.N.M Azeem Iqrah B.Sc.Eng (Hons), C&G (Gdip)Skills College of Technology

Introduction

• Reinforced concrete is a composite material, consisting of steel reinforcing bars embedded in concrete.

• Concrete has high compressive strength butlow tensile strength.

• Steel bars can resist high tensile stresses but will buckle when subjected to comparatively low compressive stresses.

Introduction

• Steel bars are used in the zones within a concrete member which will be subjected to tensile stresses.

• Reinforced concrete is an economical structural material which is both strong in compression and in tension.

• Concrete provides corrosion protection andfire resistance to the steel bars.

Basic of design

• Two limit states design for reinforced concrete in accordance to BS 8110.

1. Ultimate limit state – considers the behaviour of the element at failure due to bending, shear and compression or tension.

2. The serviceability limit state considers the behaviour of the member at working loads and is concerned with deflection and cracking.

Material properties - concrete

• The most important property is the compressive strength. The strength may vary due to operation such as transportation, compaction and curing.

• Compressive strength is determined by conducting compressive test on concrete specimens after 28 days of casting.

• Two types of specimen: (1) 100 mm cube (BS standard), and (2) 100 mm diameter by 200 mm long cylinder.

Characteristic compressive strength ofconcrete

• Characteristic strength of concrete is defined as the value below which no more than 5 percent of the test results fall.,

Characteristic compressive strength(fcu) of concrete

Chanakya Arya, 2009. Design of structural elements 3rd edition, Spon Press.

Cylinder strength

Cube strength

• Concrete strength classes in the range of C20/25and C50/60 can be designed using BS 8110.

Stress-strain curve for concrete

Stress strain curve for concrete cylinder

(Chanakya Arya, 2009. Design of structural elements 3rd edition, Spon Press.)

Idealized stress strain curve for concrete in the BS8110

Material properties of steel• Idealized stress-strain curve for steel.1. An elastic region,2. Perfectly plastic region (strain hardening of steel is

ignored)

BS 8110, 1997

Durability (clause 3.1.5, BS 8110)

• Durability of concrete structures is achieved by:

1. The minimum strength class of concrete2. The minimum cover to reinforcement3. The minimum cement content4. The maximum water/cement ratio5. The cement type or combination6. The maximum allowable surface crack

width

Fire protection (clause 3.3.6, BS8110)

• Fire protection of reinforced concrete members is largely by specifying limits for:

1. Nominal thickness of cover to thereinforcement,

2. Minimum dimensions of members.

Concrete cover for fire resistance

BS 8110, 1997

Minimum dimension for reinforcedconcrete members for fire resistance

BS 8110, 1997

Beams (clause 3.4, BS8110)

• Beams in reinforced concrete structures can be defined according to:

1. Cross-section2. Position of reinforcement3. Support conditions

Beam design

• In ultimate limit state, bending is critical for moderately loaded medium span beams. Shear is critical for heavily loaded short span beams.

• In service limit state, deflection will be considered.

• Therefore, every beam must be design against bending moment resistance, shear resistance and deflection.

Types of beam by cross section

Rectangular section L-section T-section

•L- and T-section beams are produced due to monolithic construction between beam and slab. Part of slab contributes to the resistance of beam.•Under certain conditions, L- and T-beams are moreeconomical than rectangular beams.

Types of beam by reinforcementposition

Singly reinforced Doubly reinforced

• Singly reinforced – reinforcement to resist tensile stress.• Doubly reinforced – reinforcement to resist both tensile

and compressive stress.• Compressive reinforcement increases the moment

capacity of the beam and can be used to reduce the depth of beams.

Notation for beam (clause 3.4.4.3, BS 8110)b

hd

d’

AS

A’S

Design for bending

M ≤ MuMaximum moment on beam ≤ moment capacity of

the sectionThe moment capacity of the beam is affected by:1. The effective depth, d2. Amount of reinforcement,3. Strength of steel bars4. Strength of concrete

Singly reinforced beam

Moment capacity of singly reinforcedbeam

Fcc

Fst

z

Force equilibrium Fst = Fcc

Fcc = stress x area=

Moment capacity of the section

Singly reinforced beam

• IfThen the singly reinforced section is sufficient to

resist moment.Otherwise, the designer have to increase the

section size or design a doubly reinforced section

Doubly reinforced beam

• IfThe concrete will have insufficient strength in

compression. Steel reinforcement can be provided in the compression zone to increase compressive force.

Beams which contain tension and compression reinforcement are termed doubly reinforced.

Doubly reinforced beam

M = Fsc (d-d’) + Fcc z

Example 3.2 Singly reinforced beam(Chanakya Arya, 2009)

• A simply supported rectangular beam of 7 m span carries characteristic dead (including self-weight of beam), gk and imposed, qk, loads of 12 kN/m and 8 kN/m respectively. Assuming the following material strengths, calculate the area of reinforcement required.


Compression reinforcement is not required


Provide 4H20, (As = 1260 mm2)

Cross section area for steel bars (mm2)

Example 3.7 Doubly reinforced beam(Chanakya Arya, 2009)

• The reinforced concrete beam has an effective span of 9m and carries uniformly distributed dead load (including self weight of beam) and imposed loads as shown in figure below. Design the bending reinforcement.

Example 3.7 Doubly reinforced beam (ChanakyaArya, 2009)


Compression reinforcement is required


Failure mode of beam in beam

• The failure mode of beam in bending depends on the amount of reinforcement.

(1)under reinforced reinforced beam – the steel yields and failure will occur due to crushing of concrete. The beam will show considerable deflection and severe cracking thus provide warning sign before failure.

(2)over-reinforced – the steel does not yield and failure is due to crushing of concrete. There is no warning sign and cause sudden, catastrophic collapse.

Shear (clause 3.4.5, BS8110)• Two principal shear failure mode:(a)diagonal tension – inclined crack develops and

splits the beam into two pieces. Shear link should be provide to prevent this failure.

(b)diagonal compression – crushing of concrete. The shear stress is limited to 5 N/mm2 or 0.8(fcu)0.5.

Shear (clause 3.4.5, BS8110)• The shear stress is determined by:

• The shear resistance in the beam is attributed to (1) concrete in the compression zone, (2) aggregate interlock across the crack zone and(3) dowel action of tension reinforcement.

Shear (clause 3.4.5, BS8110)

• The shear resistance can be determined using calculating the percentage of longitudinal tension reinforcement (100As/bd) and effective depth


• The values in the table above are obtained based on the characteristic strength of 25 N/mm2. For other values of cube strength up to maximum of 40 N/mm2, the design shear stresses can be determined by multiplying the values in the table by the factor (fcu/25)1/3.


Shear (clause 3.4.5, BS8110)• When the shear stress exceeded the 0.5c,

shear reinforcement should be provided.(1) Vertical shear link(2) A combination of vertical and inclined

bars.


• Sv ≤ 0.75d

Example 3.3 Design of shear reinforcement(Chanakya Arya, 2009)

• Design the shear reinforcement for the beam using high yield steel fy = 500 N/mm2 for the following load cases:

1. qk = 02. qk = 10 kN/m3. qk = 45 kN/m

Example 3.3 Design of shear reinforcement(Chanakya Arya, 2009)

Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009)



Provide nominal shear link

= 0.3

• The links spacing Sv should not exceed 0.75d (0.75*547 = 410 mm).

• Use H8 at 300 mm centres.


Example 3.3 Design of shear reinforcement (Chanakya Arya, 2009) Case 3 (qk = 45 kN/m)


Provide H8 at 150 mm centres.

Nominal shear links can be used from mid-span to position v = 1.05 N/mm2, to produce an economical design

Provide H8 at 300 mm centres. For 2.172 m either side from centres.

Reinforcement detailing.


Deflection

• For rectangular beam,1. The final deflection should not exceed span/2502. Deflection after construction of finishes and

partitions should not exceed span/500 or 20mm, whichever is the lesser, for spans up to 10 m.

BS 8110 uses an approximate method based onpermissible ratios of the span/effective depth.

Deflection (clause 3.4.6.3)

• This basic span/effective depth ratio is used in determining the depth of the reinforced concrete beam.

Reinforcement details (clause 3.12, BS8110)

• The BS 8110 spell out a few rules to follow regarding:

1. Maximum and minimum reinforcement area

2. Spacing of reinforcement3. Curtailment and anchorage of

reinforcement4. Lapping of reinforcement

Reinforcement areas (clause 3.12.5.3and 3.12.6.1, BS 8110)

• Minimum area of reinforcement is provided to control cracking of concrete.

• Too large an area of reinforcement will hinder proper placing and compaction of concrete around reinforcement.

• For rectangular beam with b (width) and h (depth), the area of tensile reinforcement, As should lie:

• 0.24% bh ≤As ≤ 4% bh• 0.13% bh ≤As ≤ 4% bh

for fy = 250 N/mm2

for fy = 500 N/mm2

Spacing of reinforcement (clause3.12.11.1, BS 8110)

• The minimum spacing between tensile reinforcement is provided to achieve good compaction. Maximum spacing is specified to control cracking.

• For singly reinforcement simply supported beam the clear horizontal distance between tension bars should follow:

• hagg + 5 mm or bar size≤ sb≤ 280 mm fy = 250 N/mm2

• hagg + 5 mm or bar size≤ sb≤ 155 mm fy = 500N/mm2 (hagg is the maximum aggregate size)

Curtailment (clause 3.12.9, BS 8110)

• The area tensile reinforcement is calculated based on the maximum bending moment at mid- span. The bending moment reduces as it approaches to the supports. The area of tensile reinforcement could be reduced (curtailed) to achieve economic design.

Curtailment (clause 3.12.9, BS 8110)

Simply supported beam

Continuous beam

(Chanakya Arya, 2009)

Anchorage (clause 3.12.9, BS 8110)• At the end support, to achieve proper anchorage

the tensile bar must extend a length equal to one of the following:

1. 12 times the bar size beyond the centre line ofthe support

2. 12 times the bar size plus d/2 from the face of support

(Chanakya Arya, 2009)

Anchorage (clause 3.12.9, BS 8110)• In case of space limitation, hooks

or bends in the reinforcement can be use in anchorage.

• If the bends started after the centre of support, the anchorage length is at least 4 but not greater than 12.

• If the hook started before d/2 from the face of support, the anchorage length is at 8r but not greater than 24.

Continuous L and T beam• For continuous beam, various loading

arrangement need to be considered to obtain maximum design moment and shear force.

Continuous L and T beam

• The analysis to calculate the bending moment and shear forces can be carried out by

1. using moment distribution method2. Provided the conditions in clause 3.4.3 of BS

8110 are satisfied, design coefficients can be used.

Clause 3.4.3 of BS 8110: Uniformly-loaded continuous beams with approximately equal spans: moments and

shears

L- and T- beam

• Beam and slabs are cast monolithically, that is, they are structurally tied.

• At mid-span, it is more economical to design the beam as an L or T section by including the adjacent areas of the slab. The actual width of slab that acts together with the beam is normally termed the effective flange.

L- and T-beam

• At the internal supports, the bending moment is reversed and it should be noted that the tensile reinforcement will occur in the top half of the beam and compression reinforcement in the bottom half of the beam.

Clause 3.4.1.5: Effective width offlanged beam

Effective span – for continuous beam the effective span should normally taken as the distance between the centres of supports

L- and T- beam

• The depth of neutral axis in relation to the depth of the flange will influence the design process.

• The neutral axis

• When the neutral axis lies within the flange, the breadth of the beam at mid-span(b) is equal to the effective flange width. At the support of a continuous beam, the breadth is taken as the actual width of the beam.

Engineering

Beam design