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Lecture 17 Shear Design

- July 16, 2003
- CVEN 444

Lecture Goals

- Shear beam example for a beam
- Shear design for slab
- Slab design example

Example Design of Stirrups to Resist Shear

From flexural design

fc 4000 psi fy 60 ksi wsdl

1.2 k/ft wll 1.8 k/ft fys 40 ksi wb

0.5 k/ft

will use either a 3 or 4 stirrup

Example Design of Stirrups to Resist Shear

Consider the pattern loading on the beam and

determine the envelope of absolute maximum shear

along the beam for a symmetric beam with

uniformly distributed loads, a straight line

drawn between the maximum at the end and midspan

is adequate.

Example Design of Stirrups to Resist Shear

The maximum shear is where,

Example Design of Stirrups to Resist Shear

The maximum shear is Note

Multiply by 1.15 for end moments _at_ face of 1st

internal support when using ACI shear coefficient

1.15 Vumax (section 8.3)

Example Design of Stirrups to Resist Shear

The wall is an interior section so the

coefficient is 1.0. For shear the reduction

factor, f, is 0.75.

How do you get maximum shear the center?

Example Design of Stirrups to Resist Shear

There is no pattern load for dead loads Vdl 0

_at_ center

Example Design of Stirrups to Resist Shear

There is a pattern load for live loads at the

center of the beam

Example Design of Stirrups to Resist Shear

Compute the Vu max at the center

Example Design of Stirrups to Resist Shear

The shear envelope can be constructed using the

values of two maximum at the two location end and

the center.

Example Design of Stirrups to Resist Shear

Calculate the equation of the line to bound the

shear force and

The slope of the shear forces.

Example Design of Stirrups to Resist Shear

Calculate the equation of the line to bound the

shear force and

1

Example Design of Stirrups to Resist Shear

Calculate the capacity of the concrete

2

Example Design of Stirrups to Resist Shear

Calculate 0.5 of Vc to check to see if shear

reinforcement is needed.

2

114.8 k gt 0.5Vc Need shear reinforcement

Example Design of Stirrups to Resist Shear

Determine the stirrup spacing requirement, Av

for the calculations

3

The area, Av, is twice the area of the bars Ab

Example Design of Stirrups to Resist Shear

The minimum spacing (11.5.5.3 ACI)

3

Example Design of Stirrups to Resist Shear

The allowable maximum spacing

3

The maximum spacing is 13.1 in.

Example Design of Stirrups to Resist Shear

Check the maximum allowable steel shear force

4

Example Design of Stirrups to Resist Shear

Check the maximum allowable steel shear force

4

Reinforcements can be used for shear

reinforcement. The beam does not need to be

redesigned.

Example Design of Stirrups to Resist Shear

Strength requirement is given as

Instead of solving for s, we can plot the Vc

Vs, where

Example Design of Stirrups to Resist Shear

Using this technique (ACI 11.3.1), various Av and

spacing s can be used. The maximum V is

determined at the distance,d from the wall.

Example Design of Stirrups to Resist Shear

The shear force are

Example Design of Stirrups to Resist Shear

This is one possibly form to check

Example Design of Stirrups to Resist Shear

There always going to be a shear reinforcement

close to the support. Use the minimum spacing, 4

in., so that the first stirrup has 4 in. Spacing

can be computed as

Example Design of Stirrups to Resist Shear

If we are using 8 4 stirrups _at_ 7 in. spacing,

(7 in. is less than 7.92 in.) So,

Example Design of Stirrups to Resist Shear

Compute the location of the point and

find Compute Vn

Example Design of Stirrups to Resist Shear

Compute the next spacing

Use s 9 in., which is find for 4 bar. Trying

to fit the reinforcement inside the beam.

Example Design of Stirrups to Resist Shear

If we are using 6 4 stirrups _at_ 9 in. spacing, 9

in. is less than 11.3 in. So,

Example Design of Stirrups to Resist Shear

Compute the location of the point and

find Compute Vn

Example Design of Stirrups to Resist Shear

Use a 3 bar for

Use s 12 in., because the smax is 13.1 in.

Example Design of Stirrups to Resist Shear

If we are using 8 3 stirrups _at_ 12 in. spacing,

12 in. is less than 13.1 in. So,

Example Design of Stirrups to Resist Shear

Compute the location of the point and find This

is at the middle of the beam. Under Vc/2 no

stirrups are need other than the minimum.

Example Design of Stirrups to Resist Shear

Example Design of Stirrups to Resist Shear

There is a mistake for the problem! What is the

error?

The spacing of the 3 bar is 12 in. and the max

spacing between bars is 11.7 in., so go back and

redesign. Easy way would be to use 4 instead of

3 bars.

Example Design of Stirrups to Resist Shear

Discontinuities at Bar Cutoff

Prohibits flexural bar cutoffs in zone of

flexural tension, unless 1 of the following is

satisfied.

ACI 12.10.5

(1) (2)

Extra stirrups are provided at the cutoff points.

(See Sec. 12.10.5.2 for details)

Discontinuities at Bar Cutoff

Prohibits flexural bar cutoffs in zone of

flexural tension, unless 1 of the following is

satisfied.

ACI 12.10.5

For No 11 bars smaller Increase shear

strength is required when bars are cutoff in a

tension zone.

(3)

Joist Design

Refer to earlier notes for general information on

joist layout. ACI Sec. 8.11 Joist

construction requirements

Flat slab reinforcement is calculated for bending

or minimum reinforcement for shrinkage and

temperature.

(1)

(ACI Sec 7.12.2 )

Joist Design

Shear Design of Joist Ribs (Joist - Section 8.11)

(2)

Joist Design

Joist Design

One-Way Slab Design

Design of one slabs is like design of parallel

12 beams.

Thickness of One-Way Slabs

Minimum thickness for solid one-way slabs not

supporting or attached or attached to partitions,

etc. Likely to be damaged by large deflections

ACI Table 9.5(a)

One-Way Slab Design

Thickness of One-Way Slabs

The table calculates the minimum thickness t ( l

span length in inches) (normal weight concrete

fy 60 ksi see code for modification factors)

One-Way Slab Design

Thickness of One-Way Slabs Table A-14 tmin,

when damage to non-structural components may

occur

One-Way Slab Design

Thickness of One-Way Slabs

Fire Rating

This is equal to the number of hours for

unexposed surface to rise a set amount usually

250 o F

3.50 in. 1 hour 5.00 in.

2 hours 6.25 in. 3 hours

Cover for Slab Reinforcement

ACI Sec. 7.7.1 (min. cover for corrosion

protection)

( 1.) Concrete exposed to earth or weather.

5 and smaller 1.5 in. 6 and larger 2.0

in.

( 2.) Concrete not exposed to earth or weather.

11 and smaller 0.75 in.

Min. covers for fire ratings should also be

considered.

One-Way Slab Design

Reinforcement

Typical Reinforcement in a one-way slab

One-Way Slab Design

Cutoffs

If requirements for use of ACI Moment

Coefficients

Figure 10.9 text one-way slab (ref. ACI

Committee 315 ACI Detail Manual 1980)

One-Way Slab Design

Need to confirm thickness is adequate for one-way

shear. Difficult to place shear reinforcement in

a slab. Minimum area of shear reinforcement

required in slabs if

ACI Sec. 11.5.5.1

ACI Eqn. 11-3

Usual use

One-Way Slab Example

The cross section of a continuous one-way solid

slab in a building is shown. The slabs are

supported by beams that span 24 ft. Between

simple supports. The dead load on the slabs is

that due to self-weight plus 60 psf The live

load is 120 psf. Design the continuous slab and

draw a detailed section. Given fc 3 ksi, fy

40 ksi.

One-Way Slab Example

Determine the thickness of the slab.

Minimum thickness of interior bay

One-Way Slab Example

Use h 6 in.

Dead weight

One-Way Slab Example

Determine the load on the floor

For slab design r is seldom gt 0.01. Use c/d 0.2

One-Way Slab Example

Find the coefficient of the moment diagram

The maximum moment is

One-Way Slab Example

Find the design d for a one-foot strip

If b 12-in. then d 3.46-in., which for c/d

0.2, so d 5-in., the slab is OK.

One-Way Slab Example

Find the coefficient of the shear

The maximum shear is

One-Way Slab Example

Check the shear capacity of the slab

Use h 6-in., d 5-in. and wu 0.354 k/ft

One-Way Slab Example

Minimum about of steel is (use ACI 7.12 )

Moment capacity of the slab (12-in. beam)

Assume

One-Way Slab Example

Compute the moments

Moment capacity of the beam

One-Way Slab Example

Compute the moments

One-Way Slab Example

Check the assumption

Assumption will work!

One-Way Slab Example

Use 4 bar Ab 0.2 in2 The maximum spacing ACI

7.6.4

maximum spacing

The spacing on the first location

One-Way Slab Example

Select 15 in. for the spacing to calculate the

provided area.

One-Way Slab Example

Actual spacing.

One-Way Slab Example

Summary