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Construcţii Metalice

Licenţa

Steel

1. Stress-strain curve for steel: Plot the stress-strain curves for a mild carbon steel and for

a high strength steel without yield plateau; mark the characterisc points

Alungire specifica, [%]

Efo

rt u

nitar,

N/m

m2

Stress-strain curve for mild carbon steel

Stress-strain curve for high strength steel without yield plateau

Nominal values of yield strength fy and tensile strength fu for the mild carbon steel are as

follows:

fy = Reh

fu = Rm.

Nominal values of yield strength fy and tensile strength fu for a steel without yield plateau are

as follows:

fy = Rp0.2

fu = Rm

Rp0.2

0.2 Alungire specifica, [%]

Efo

rt u

nitar,

[N

/mm

2]

[N/m

m2

]

Rm

E – Young’s modulus (elastic modulus)

Ae – Elongation at yielding

Ag – Total elongation at yielding

Agt – Total elongation at fracture point

A - The elongation at fracture

At - The total elongation at fracture

Rel - Lower yield strength

ReH – Upper yield strength

Rm - Tensile strength

Note: If there is no yield plateau, the yield

strength at 0.2 % elongation is considered

(Rp0.2)

2. Typical steel grades are described as S--- J--- Z--. Indicate three different steel grades

and explain the significance of the notations.

The letters used for the definition of steel grades indicate:

S--- the yield strength in newtons per square millimetre (yield strengt in N/mm2)

J-- the materials toughness by reference to Charpy impact test values (in J, for a specified

temperature)

Z-- Through thickness ductility, in %, (average reduction in area at failure), represents the

capacity of the material to avoid the lamelar tearing when loaded perpendicular to the surface.

Examples:

S235 J0 Z15: Steel with yield strength of 235 N/mm2, toughness of minimum 27 J at 0ºC,

reduction in area at failure of minimum 15%.

S275 J2 Z25: Steel with yield strength of 275 N/mm2, toughness of minimum 27 J at

-20ºC, reduction in area at failure of minimum 25%.

S355 JR Z35: Steel with yield strength of 355 N/mm2, toughness of minimum 27 J at +20ºC,

reduction in area at failure of minimum 35%.

3. What is strain aging of steel? What is strain hardening of steel? Describe

comparatively using stress - strain curves a S235 steel and a S460 steel.

Strain hardening is when the steel is strained beyond the yield point. An increasing stress is

required to produce additional plastic deformations. This phenomenon depends on the

properties of the steel.

Strain aging is a process of increasing the resistance of the steel. If the aging takes place at the

ambient temperature, the process is called natural aging, and if it takes place at elevated

temperature is called artificial aging. Aging increases the brittleness of steel, by reducing its

ductility.

Figure shows comparatively the stress-strain curve before and after the strain aging or strain

hardening develop.

Strain aging vs. strain hardening

4. Explain the term „ductility” which is associated to steel material.

Ductility of the steel represents its ability to deform plastically, without breaking. For steel

material, a minimum ductility is required that should be expressed in terms of limits for:

- the ratio fu / fy of the specified minimum ultimate tensile strength fu to the specified

minimum yield strength fy ; Recommended value fu / fy ≥ 1.10;

- the elongation at failure; Recommended value: elongation at failure not less than 15%;

- elongation at the end of yield plateau; Recommended value ε ≥1,5%.

fu

fy

E

Strain [%]

Str

ess, [N

/mm

2]

Global analysis

5. What is the cross section class of a structural steel member? Define the cross-section

classes and the parameters that define the class of the cross section.

Strength and stability design of structural steel bar members depends on the class of the cross

section. Cross section class is defined by the proportions of the cross section and indicates the

slenderness of the walls. The classification is given by the width-to-thickness ratio. There are

four classes:

- class 1: “plastic”, cross-section can form a plastic hinge with the required rotational capacity

for plastic analysis

- clasa 2: “compact”, cross-sections although is able to develop a plastic moment, has limited

rotational capacity and is therefore unsuitable for structures designed by plastic analysis

- clasa 3: “elastic”, the calculated stress in the extreme compression fibre can reach yield but

local buckling prevents the development of the plastic moment resistance.

- clasa 4: “elastic”, with reduced section (effective section).

fy

Moment

fy

Moment

fy

Moment

Mel

fy

Moment

Mel

Model

comportare

Distributia

ef. unitareCapacitate de rotire Clasa

1

1

1

1

1

1

1

1

Suficienta

Limitata

Nu

Nu

MMpl

MMpl

MMpl

MMpl

1

2

3

4

Momentul plastic

pe sectiunea plina

Momentul plastic

pe sectiunea plina

Momentul elastic

pe sectiunea plina

Momentul plastic

pe sectiunea efectiva

Mpl

Mpl

Mpl

Mpl

Mel Momentul capabil elastic

Mpl Momentul capabil plastic

M Momentul din incarcari Rotirea sectiunii (curbura)

Rotirea (curbura) sectiunii necesara pentru a permite distributia eforturilor in domeniul plasticpl

fy

Moment

fy

Moment

fy

Moment

Mel

fy

Moment

Mel

Model

comportare

Distributia

ef. unitareCapacitate de rotire Clasa

1

1

1

1

1

1

1

1

Suficienta

Limitata

Nu

Nu

MMpl

MMpl

MMpl

MMpl

1

2

3

4

Momentul plastic

pe sectiunea plina

Momentul plastic

pe sectiunea plina

Momentul elastic

pe sectiunea plina

Momentul plastic

pe sectiunea efectiva

Mpl

Mpl

Mpl

Mpl

Mel Momentul capabil elastic

Mpl Momentul capabil plastic

M Momentul din incarcari Rotirea sectiunii (curbura)

Rotirea (curbura) sectiunii necesara pentru a permite distributia eforturilor in domeniul plasticpl

6. What is the second order global analysis? What are the geometric imperfections

(global, local)? How these imperfections can be included in a second order analysis of

a structure made from bar members?

Second order global analysis takes into account the influence of the deformation of the

structure and, therefore, reference must be made to the deflected geometry under load. Second

order effects increase not only the deflections but also the moments and forces beyond those

calculated by first-order analysis. The effects of the deformed geometry cannot be ignored

when:

10crcr

Ed

F

F

where:

- Fcr is the elastic critical load for global instability, based on initial elastic stiffness

- Fed is the design load on the structure.

Geometrical imperfections take into account the lack of straightness of the member, section

shape variation, etc. Global imperfection can be modeled by means of out-of-plumbness or

alternatively, by means of a system of equivalent horizontal forces. The inclination from the

vertical is given by the angle , where:

0 h m

where:

0 is the basic value, 0 = 1/200

h is the reduction coefficient considering the height of the columns, h

m the number of columns in a row – for a portal the number of columns in a single frame

7. What are the conditions for the application of a first order plastic analysis? What are

the conditions for the application of a second order plastic analysis?

The choice of first-order plastic analysis may be governed by the conditions of material and

sections ductility, symmetry of the cross sections, stability of the elements in compression

or/and bending. First-order plastic analysis requires the verification of the flexibility (second

order effects), measured by the factor cr.

For a plastic analysis, if

15crcr

Ed

F

F

then the effects of the deformed geometry cannot be ignored and a second order plastic

The conditions for the application of a second order plastic analysis are similar to the

conditions of application of the first order analysis but when the factor cr is larger than 15.

For this type of analysis, are combined the conditions of application of the first order plastic

analysis with the conditions of application of second order elastic analysis.

Connections

8. Describe standard welding methods. What types of stresses develop in fillet welding

and how can be evaluated?

a) Metal arc welding (MMA). The principle of the technology: heat is generated by an

electric arc between an electrode and the work piece, which melts and fills the weld pool.

Neutral shielding gases and/or shielding fluxes are used for protection of the weld pool

from atmospheric contamination

b) Metal Inert Gas Welding (MIG/MAG). The principle of the technology: arc welding

process, in which the arc between the electrode wire and the work piece heats and melts

both the work pieces edges and the electrode wire. The weld is shielded by an external gas

(eg. Argon).

c) Tungsten Inert Gas welding (TIG). The principle of the technology: welding process in

which heat is generated by an electric arc between a tungsten non-consumable electrode

and the work piece. The heat produced by the arc melts the work pieces edges and joins

them.

d) Oxyacetylene Welding (OW). The principle of the technology: a Gas Welding process

using a combustion mixture of acetylene and oxygen for producing gas welding flame.

The hot flame fuses the filler rod and the edges of the welded parts, which are joined

together forming a weld.

A uniform distribution of stress is assumed on the throat section of the weld, leading to the

normal:

Stresses on the throat section of a fillet weld

The design resistance of the fillet weld will be sufficient if the following are both satisfied:

,

where:

fu is the nominal ultimate tensile strength of the weaker part joined;

βw is the appropriate correlation factor

9. What are the failure modes for the bolted connection in the figure? Describe the

verification procedure.

NN

N

N

In case of bolted connections loaded in shear, the design load should is the minimum of the

design shear resistance and the design bearing resistance. These types of connections can

therefore fail by:

- shear of the bolt

- bearing of the plate

- rupture of the net area

The design shear resistance for each failure mode can be evaluated as follows:

- Shear resistance:

where

- v: factor

- fub : ultimate tensile strength of the bolt

- A : is the tensile stress area of the bolt

- γM2 : partial safety factor

- Bearing resistance:

where

- k1 : factor;

- ab : factor;

- fu : ultimate tensile strength of the plates

- d : nominal diameter of the bolt

- t is the smallest of the connected plates thickness

- γM2 : partial safety factor

- Tension resistance:

where

- fu : ultimate tensile strength of the plates

- Anet : net area of the plate

- γM2 : partial safety factor.

10. Describe the slip-resistant bolted connection. Give an example and explain the design

procedure.

In case of slip resistant bolted connections, the steel plates are tightened together by

preloading the bolts. The forces are transferred between the connected plates by friction.

The design slip resistance of a preloaded bolted connection depends on the friction coefficient

μ and preloading force in the bolt, Fp.C.

The values of the friction coefficient μ vary between 0.2 and 0.5.

The design slip resistance of a preloaded bolt class 8.8 or 10.9 should be taken as:

where

ks : coefficient, depends on the type of bolt holes

n: number of friction surfaces

μ: friction coefficient

- γM3 : partial safety factor

- Fp,C : the preloading force

11. Detail a bolted splice plate connection of a beam with gusset plates on flanges and

web

12. For the bolted joint in the figure, describes the basic components:

The evaluation of the beam-to-column joint properties, as presented in EN 1993, is based on

the component method. According to this method, the joint is divided in three zones:

- zone loaded in tension;

- zone loaded in compression;

- zone loaded in shear.

For calculation of strength and stiffness of the specific bolted joint presented in the figure, the

following components can be introduced:

- column web panel in shear (1);

- column web in compression (2);

- elements in tension for each bolt row:

Column flange in bending (3);

End plate in bending (4);

Bolts in tension (5);

Column web in tension (6);

Beam web in tension (7).

(1) (2) (3) (4)

(5) (6) (7)

13. What is a semi-rigid joint? What is a partial strength joint?

Framed structures are usually designed on the basis that the joints are either pinned or rigid.

However, the real behavior of beam-to-column joints is between these two limits, or semi-

rigid. Considering the rotational response of the joint, there are three possible cases:

- when the stiffness of all components of the joint is large, the joint is stiff and there are no

relative rotations between the connected elements. The joint can be considered rigid (Figure

a).

- when the stiffness of the joint is low, the joint is very flexible and can be considered pinned

(Figure b);

- for intermediate situations, where the stiffness is between the two extremes, there is a

relative rotation between the connected elements (Figura c). In this case, the joint is semi-

rigid.

a) Rigid joint b) Pinned joint c) Semi-rigid joint

Types of joints

Joint stiffness classification

Considering the strength of the joint, there are three possible cases:

- full strength joints

- partial strength joints

- pinned joints.

The term “full strength” describes the strength of the joint relative to the strength of the

connected element. If bending capacity of the joint is less than the capacity of the beam, then

the joint is classified as partial-strength. Mj

Mj.Rd

Rezistenţă totală

Articulat

Rezistenţă parţială

Limitele pentru rezistenţă

Rezistenţa nodului

Joint strength classification

Elements

14. For the element loaded in tension and connected with bolts (see figure), indicate the

verifications in the gross cross section and the net cross section.

The design value of the tension force NEd at each cross section should:

,

1.0Ed

t Rd

N

N

EdN : design value of the tension force;

,t RdN : design tension resistance Nt,Rd.

For sections with holes, the design value of the tension resistance is:

, , ,min( , )t Rd pl Rd u RdN N N

In the gross cross section:

0

,

y

pl Rd

M

AfN

;

01.0M

In the net area:

2

,

0.9 net uu Rd

M

A fN

;

21.25M

N N

N

N

15. What are the European buckling curves? How is made the verification of buckling

resistance for an element loaded under uniform axial force?

Evaluation of the design resistance of elements in compression according to EN 1993-1-1 is

based on the European buckling curves. According to SR EN 1993-1-1, there are five

buckling curves (a0, a, b, c si d), depending on the type of cross section and axis of buckling.

A compression member should be verified against buckling as follows:

Where

- NEd is the design value of the compression force;

- Nb,Rd is the design buckling resistance of the compression member.

For class 1, 2 and 3 cross-sections, the design buckling resistance of a compression member

should be taken as:

For class 4 cross-sections, the design buckling resistance of a compression member should be

taken as:

where χ is the reduction factor for the relevant buckling mode.

The value of χ for the appropriate non-dimensional slenderness λ should be determined from

the relevant buckling curve according to:

where:

and where for class 1, 2 and 3 cross sections:

α is imperfection factor;

Ncr is the elastic critical force for the relevant buckling mode based on the gross cross

sectional properties.

Imperfection factor α depends on the buckling curve.

16. Present the steel column base realized as a pinned joint. The column has a H section.

Explain the verification procedure for anchor bolts.

Pinned column bases can be made with 2 anchoring bolts made from round steel and a base

plate. In this case, the verification of the anchor bolts sgould take into account the interaction

between shear force and axial force (when is positive):

2 2

max max

, ,t Rd v Rd

N k Vm

F F

where:

3 bf

bi

Rk

R , Rf

b and Ri

b are the shear resistance and tensile resistance of the anchor steel

Ft,Rd is the design tension resistance of the anchor bolt

Fv,Rd is the design shear resistance of the anchor bolt (nf = 1)

Nmax and Vmax are the maximum values of the base reactions (axial force and shear force).

If the axial force is negative (compression at the base of the column), the verification should

be based on the shear force only.

17. Describe the column base realized as a rigid joint. The column has a H cross section.

Explain the verification procedure for anchor bolts.

A rigid connection of the column end can be done by means of a stiff end plate, vertical

stiffeners and minimum 4 anchoring bolts located in the in the outstand of the base plate. The

plan dimensions of the base plate should be calculated so that the resistance of the concrete

block beneath the base plate is not exceeded. In order to avoid the transfer of the shear forces

through the anchor bolts and to increase the stiffness of the joint, the column may be

embedded in concrete. The required embedment length is at least 50% of the column cross

section height. In this case, only the axial force and the bending moment need to be

considered in the verification of the anchor bolts.

18. What are the stress and strength verifications for a class 4 web of a plate girder?

The verification of the plate girders with slender webs (class 4) should take into account the

fact the web is prone to local buckling.

(a)

(b) (c)

Buckling of slender under: (a) compression; (b) bending; (c) shear

The web buckles when critical at the attainment of the critical buckling stress:

Ed cr

Ed cr

where

- cr is the critical normal stress

- cr is the critical shear stress

In general, any cross-section of a plate girder will be subjected to bending moment in addition

to shear. Therefore, the verification procedure should allow for moment/shear interaction.

The presence of transverse and/or longitudinal stiffeners may limit or even prevent local

buckling.

Structures

19. For the trapezoidal truss girder shown in the figure, describe the configuration, the

static system and joint details for upper and lower chords when the elements are

welded.

There are different truss girder configurations, depending on the span size, intensity of gravity

loads, etc. The next figure shows a trapezoidal truss girder with diagonals and vertical

members (modified Warren truss).

If the diagonals and vertical members are made from pairs of angles, then they can be

connected to upper and lower chord by fillet welds and gusset plates, see details.

Det. A Det. B

A

B

20. Present the bracing system for a single story portal frame building with one span and

five bays and pinned column bases. Justify the necessity of bracings and their effects

on the structure.

Portal frames of single story buildings can be made of I section columns and beams, rigid

beam to column connections and pinned column bases. In this case, portal frame provides the

lateral stability against lateral loads on the transversal direction. On the longitudinal direction,

the lateral stability can be achieved by vertical bracing systems. In order to allow the transfer

of the lateral loads from the roof to the columns and further to the foundations, braces may

also be required in the roof.

If vertical braces are used in the end gables in order to increase the lateral stiffness, then they

should be connected by braces in the roof.