Appunti di Sismica

FOR NTC

The first hoop shall be placed not more than 50 mm from the beam end sec�on (see Figure 5.6).

• At least 2+2 con�nuous bars φ 14

• 1

Cri�cal zone:

• ≥

2

1

Always

• ≥

4

1

in the span at the extremes

• ≥

4

Prescrip�ons given for bar anchorage

•

In each sec�on of the beam, unless jus�fica�ons demonstrate that the collapse modes of the sec�on are

consistent with the duc�lity class adopted, the geometric ra�o Ӏ rela�ng to the tension reinforcement,

regardless of whether the tension reinforcement is that at the upper edge of sec�on As or that at the lower

edge of sec�on Ai, must be included within the following limits:

1.4 3.5

< < + ℎ

Where is the geometric ra�o rela�ng to the tensioned reinforcement, equal to or

( ∙ ℎ) ( ∙ ℎ),

is the geometric ra�o rela�ng to the compressed reinforcement; is the characteris�c yield stress

of the steel (in MPa).

In Eurocode 8

(4) The requirement specified in (3)P of this subclause is deemed to be sa�sfied, if the following condi�ons

are met at both flanges of the beam:

a) at the compression zone reinforcement of not less than half of the reinforcement provided at the

tension zone is placed, in addi�on to any compression reinforcement needed for the ULS verifica�on

of the beam in the seismic design situa�on.

b) The reinforcement ra�o of the tension zone ρ does not exceed a value equal to:

0.0018

ʹ

= ρ + ∙

,

Along the en�re length of a primary seismic beam, the reinforcement ra�o of the tension zone, ρ, shall be

not less than the following minimum value ρmin:

= 0.5( )

DCH: b) at least two high bond bars with d = 14 mm shall be provided both at the top and the botom of the

b

beam that run along the en�re length of the beam; c) one quarter of the maximum top reinforcement at the

supports shall run along the en�re beam length.

Beams: prescrip�ons for shear reinforcement Within the cri�cal regions of primary

seismic beams, hoops sa�sfying the

following condi�ons shall be provided: The

diameter d of the hoops (in millimetres)

bw

shall be not less than 6 and The spacing of

hoops (in millimetres) shall not exceed

(figure). 75% of the reinforcement must be

placed within the column sec�on

Columns: geometric and reinforcement prescrip�ons The total longitudinal reinforcement ra�o ρl

shall be not less than 0,01 and not more than

0,04. In symmetrical cross-sec�ons

symmetrical reinforcement should be

provided (ρ = ρʹ). (2)P At least one

intermediate bar shall be provided between

corner bars along

each column side, to

ensure the integrity

of the beam-column

joints. (3)P The

regions up to a

distance lcr from both

end sec�ons of a

primary seismic

column shall be

considered as being

cri�cal regions. …As

regards the transversal reinforcement, both the EC8 and the NTC18 give more or less complex formulas.

(diaposi�ve 51 e 52)

Anchorage of reinforcement in a node

(1)P The part of beam longitudinal reinforcement bent in joints for anchorage shall always be placed inside

the corresponding column hoops. (2)P To prevent bond failure the diameter of beam longitudinal bars

passing through beam-column joints, dbL, shall be limited in accordance with the following expressions: …(3)

If the requirement specified in (2)P of this clause cannot be sa�sfied in exterior beam-column joints because

the depth, hc, of the column parallel to the bars is too shallow, the following addi�onal measures may be

taken, to ensure anchorage of the longitudinal reinforcement of beams:

1. The beam or slab may be extended horizontally in the form of exterior stubs

2. Headed bars or anchorage plates welded to the end of the bars may be used

3. Bends with a minimum length of 10dbL and transverse reinforcement placed �ghtly inside the bend

of a group of bars may be added.

4)P Top or botom bars passing through interior joints, shall terminate in the members framing into the joint

at a distance not less than lcr (length of the member cri�cal region) from the face of the joint.

Lesson 13 - Capacity design

In order to understand capacity design, we must remember the design approach we selected: We design in

order to control damage extension and damage patern. We select a patern that develops damage «slowly»,

distributed on the en�re structure and we avoid paterns with high concentra�on of damage that requires

unreachable levels of local duc�lity, resul�ng in sudden, britle failure. In order to atain this patern, Plas�c

hinges may form in beams only. Columns must be more resistant than beams, with good margins that is,

when plas�c hinges form in beams, columns must be fully elas�c. We must be absolutely sure that columns

will be elas�c, considering all the possible situa�ons for which a beam may be stronger than planned for

example: Overstrength due to construc�on phase errors, A bigger beam decided by workers etc. on

construc�on site, Prac�cal selec�on of the closest cross-sec�on (larger) or Margins in design …. In order to

have «strong columns, weak beams» we need to design the beam first:

1. Consider results from analysis with seismic ac�on

2. Select the beam cross sec�on (for construc�on reasons,it will be greater than the required values

from analysis)

3. Consider the maximum resis�ng moment for the cross sec�on adopted,

4. Design the columns for when the beams have reached such moment, not for the values from the

analysis, which are smaller

5. In the design of a node of columns and beams, add an addi�onal safety factor (overstrength factor)

increasing the ,

Capacity design with hyerarchy of strengths

In mul�-storey buildings forma�on of a so� storey plas�c mechanism shall be prevented, as such a

mechanism might entail excessive local duc�lity demands in the columns of the so� storey. To sa�sfy this

requirement, in frame buildings, including frame-equivalent ones,

with two or more storeys, the following condi�on should be sa�sfied

at all joints of primary or secondary seismic beams with primary

seismic columns: � ≥ 1.3 �

is the sum of the design values of the moments of

Where ∑

resistance of the columns framing the joint. The minimum value of

column moments of resistance within the range of column axial forces

produced by the seismic design situa�on should be used in this

expression; and is the sum of the design values of the

∑

moments of resistance of the beams framing the joint. When par�al strength connec�ons are used, the

moments of resistance of these connec�ons are taken into account in the calcula�on of . Note that A

∑

rigorous interpreta�on of expression requires calcula�on of the moments at the centre of the joint. These

moments correspond to development of the design values of the moments of resistance of the columns or

beams at the outside faces of the joint, plus a suitable allowance for moments due to shears at the joint

faces. However, the loss in accuracy is minor and the simplifica�on achieved is considerable if the shear

allowance is neglected. This approxima�on is then deemed to be acceptable. Implica�ons are then: a

compulsory sequence in design (beams first, then columns),a modifica�on (amplifica�on) of computed

values of internal ac�ons for columns.

What about shear?

Shear brings the cross-sec�on and the beam to fail by britle failure, it must be avoided. To do so we imagine

that plas�c hinges have developed in the beam due to seismic ac�on, so we need:

1. Compute shear corresponding to plas�c hinge moments and ver�cal loads (in the worst

combina�on),

2. Use an overstrength factor

3. Design reinforcement for shear

In this way shear reinforcement will remain «elas�c» even if plas�c hinges will form and shear will not

interfere in the ul�mate behaviour.

To compute shear corresponding to

plas�c hinge moments and

ver�cal loads we consider the

forma�on of two plas�c hinges at

the extremes of a beam. The two

plas�c hinges have formed, so the

corresponding moment is the

plas�c one, nothing else is formed,

it is all exploited. It must be verified

that the shear reinforcement is s�ll

elas�c for the shear forces created

in this condi�on. The distribu�on of

the ver�cal load ( creates

+ )

2

constraining reac�ons as if there were simple supports Having reached the plas�c hinge, the two

( ).

+

+ −

moments are present at the ends of the rod, i.e. an and an , opposite, and the two shear forces (if

the moments are reversed, the sign of the shear forces is also reversed). To calculate the seismic shear, 2

situa�ons must be considered, which correspond to 4 combina�ons: +

1. Gravita�onal + accidental + posi�ve shear ( = " + " )

+

2 −

2. Gravita�onal + accidental + nega�ve shear ( = " + " )

+

2

One of these, i.e. the worst, will give the shear to consider. The shear demand, for each direc�on and each

direc�on of applica�on of the seismic ac�ons, is obtained from the equilibrium condi�on of the beam,

considered plas�c hinged at the ends, subject to the gravita�ona