Fundamentals of structural mechanics

EK707

Compatibility torsion arises in monolithic construction when compatibility of deformation of the connected parts have to be maintained, e.g. edge beams in a normal framed building with slabs and beams […]

EK706

Equilibrium torsion is essential for the basic stability of the element or structure.

EK705

In EC2 the limit to the amount of redistribution is related to the ductility characteristics of the reinforcement used: class B or class C reinforcement – 30% class A reinforcement […]

EK699

Truss elements and two- and three-dimensional elements support only translational degrees of freedom, and therefore concentrated nodal moments cannot be applied to these elements; only concentrated forcescan be applied.

EK698

Plane stress is defined to be a state of stress in which the normal stress and the shear stresses directed perpendicular to the plane are assumed to be zero.

EK697

The reverse shear force below the flexural plastic hinge (the hinge at the location above the podium level) may be much larger than the base shear above the flexural hinge, […]

EK696

Due to the complexity of capturing backstay effects in the analysis, it may be desired to eliminate the phenomenon in the actual buildings. This can be accomplished by isolating the […]

EK695

The backstay effect is the set of lateral forces developing within a podium structure to equilibrate the lateral forces and moment of a tower extending above the podium structure. This […]

EK694

The existence of one or more underground stories causes the perimeter below-grade walls with the diaphragm of grade level to constitute of a very stiff box. In this case or […]

EK691

According to EC2, the effective span of a beam continuous over its supports should normally be taken as the distance between the centres of the supports.

EK690

According to EC2, the effective span of a simply supported beam should normally be taken as the clear distance between the faces of supports plus one-third of the beam seating […]

EK689

According to EC0, all actions originating from the selfweight of the structure may be considered as coming from one source and there is no requirement to consider different factors on […]

EK688

For reinforced concrete frame structures, movement joints at least 25mm wide should normally be provided at approximately 50m centres both longitudinally and transversely. In the top storey with an exposed […]

EK687

Movement joints may also be required where there is a significant change in the type of foundation, or the height or plan form of the structure.

EK686

Movement joints should divide the structure into a number of individual sections, and should pass through the whole structure above ground level in one plane.

EK685

The core and shear walls should preferably be distributed throughout the structure and so arranged that their combined shear centre is located approximately on the line of the resultant in […]

EK684

Lateral stability in two orthogonal directions should be provided by a system of strongpoints within the structure so as to produce a braced non-sway structure, which is stiff enough that […]

EK681

Construction rules defined for shear resistance generally apply for interface shear.

EK680

For fatigue loading, the shear resistance for adhesion must be halved.

EK679

For the general expression for interface shear, which includes the three load bearing mechanisms of adhesion, friction due to externally applied normal stress and reinforcement, the state of the horizontal […]

EK678

It is assumed that only interface reinforcement perpendicular to the interface or inclined towards the direction of the relative slip can participate in the shear transfer mechanism.

EK677

If the bar is fully utilised for tension, it cannot contribute to the shear resistance due to dowel action.

EK676

Especially for rough interfaces, shear stresses lead to crack openings with vertical displacements longitudinal strain develop in the reinforcing bars. If the reinforcement bars are sufficiently anchored at both sides […]

EK675

The bending mechanism is decisive for dowel action. The mechanism of shear is subordinate and kinking only occurs after very large interface displacements and is therefore neglectable for common building […]

EK674

With sufficient concrete cover, a multi-axial stress state develops in the concrete surrounding the reinforcing bar at both sides of the cracked interface. After increasing interface displacement, the concrete plasticizes […]

EK673

The activation of dowel action in the reinforcement bar occurs due to relative horizontal displacement of old and new concrete layer. For dowel action, it can be distinguished between the […]

EK672

For smooth interfaces, the maximum shear stress is reached after 0.01 mm relative slip.

EK671

The frictional resistance of sandblasted interfaces due to aggregate interlock fails after a relative slip of 0.03 – 0.05 mm and is independent of the applied normal stress.

EK670

An additional compressive stress acting perpendicular to the interface activates the load bearing mechanism of friction. After adhesive bond is exceeded and cracks develop along the interface, the compressive stress […]

EK669

The adhesive stress curves run constantly and then drops linearly after a relative slip of 0.02 mm. After a relative slip of 0.05 mm, no adhesive stress transfer can be […]

EK667

The main terms of interface shear resistance are adhesion, friction induced by normal stress (aggregate interlock) or by clamping of interface reinforcement. The mechanisms act at different displacement states and […]

EK666

Robustness is an ability of a structure to resist events such as fire, explosions, impact loads or the consequences of human error, without being damaged to an extent disproportionate to […]

EK665

For buildings in consequence class 1, no further consideration for robustness is necessary provided that the building has been designed adequately against normal use. For lower class 2 buildings additionalhorizontal […]

EK664

To adapt the requirements to the consequences, the classes are used to define the needed checks against accidental actions. For class 1, no specific consideration is necessary for accidental actions […]

EK663

The Eurocode uses consequence classes to differentiate efforts required to ensure sufficient safety against accidental actions. There are three defined classes CC3, CC2, and CC1, which indicate high, medium and […]

EK662

If the buckling load is more than 10 times the applied load then the system is a sway system and second order effects need to be considered. Else the second […]

EK661

If the buckling load is 10 times larger than the applied load then there is no need to include second order effects in the analysis of the global system.

EK660

According to Eurocode the second order effects may be ignored if they are less than 10 percent of corresponding first order effect.

EK659

A truss system applied on the outside of a tube system, reinforcing theexternal tubes as a stabilizing system can be used for buildings not higher than 120 storeys.

EK658

A system composed of several rectangular tubes forcing the innercolumns to interact with the facades where each tube is ended at differentheight in the building so that the influence of […]

EK657

Use of combined framework and truss system in the facade walls where the facades functions as a rectangular tube restrained in the foundation as a stabilizing system can be used […]

EK656

A framework composed of facade columns that are united to act as arectangular tube restrained in the foundation as a stabilizing system can be used for buildings not higher than […]

EK655

Fully or partially fixed columns and beams connected to a central corewith additional horizontal trusses in the middle and the top of thebuilding as a stabilizing system can be used […]

EK654

Fully or partially fixed columns and beams connected to a centralcore as a stabilizing system can be used for buildings not higher than 40 storeys.

EK653

A system of pinned columns and beams connected to a central core(either a concrete core or vertical trusses) as a stabilizing system can be used for buildings not higher than […]

EK652

A framework of fully fixed columns and beams with moment resisting joints as a stabilizing system can be used for buildings not higher than 15 storeys.

EK651

According to Eurocode 2, if the second order effects is taken into account, the equilibrium and resistance should be checked in the deformed state, including effects of cracking, non-linear material […]

EK650

Eurocode 8 set two distinct demands including a no-collapse requirement and a damage limitation requirement. The no-collapse requirement states that the structure must be designed in a way so that […]

EK649

According to Eurocode, the imperfections should be taken into account in the ultimate limit states in persistent and accidental design situations, but not in serviceability.

EK648

It is important to make sure that there are no weak spots in the building, i.e soft stories.

EK647

When evaluating continuous disturbance RMS is said to be the better indicator.

EK646

Acceleration can be defined either by peak acceleration or normalized root-mean-square (RMS) values. The peak acceleration at different frequencies can be used as an indicator for human motion thresholds. This […]

EK645

Some of the strategies to reduce the risk of accidental action include preventing or reducing action from occurring, protecting the building from the effects of the action or ensuring that […]

EK643

The friction in the soil need to be able to resist the shear forces transferred by the foundation, otherwise the foundation will slide on top of the soil.

EK642

If the building is standing on solid ground without piles it will resist overturning moment by a moment created by structures weight acting at the bearing edge.

EK641

The shear wall functions like a vertical cantilevered diaphragm, where load at the top is transferred to the bottom edge.

EK640

In structural design it is important to include redundancy in the system to ensure stability in case of accidental load where an element is eliminated.

EK639

If the critical buckling load is less than 10 times the applied vertical design load then second order effects need to be included in the structural analysis.

EK638

If the stabilizing core has openings, which is the case for elevator shafts, the openings can have a substantial influence on the deformations and shear deformations needs to be considered.

EK637

Standard deep beam theory is therefore not applicable to determinethe lateral stiffness of shear walls with openings.

EK636

Assuming fixed boundary condition at each storey the wall rigidities of high rise buildings could be computed at each storey under the followingconditions: Relatively uniform arrangement of shear walls. Relatively […]

EK635

Buildings with a height to width ratio smaller than one will mainly act as shear structures and the shear walls can be designed on a floor-to-floor basis. In taller buildings […]

EK634

Shear walls are a commonly used structural element to stabilize the building against horizontal loads and shear deformation.

EK633

Individual columns are often assumed to provide little or none stability, however, a system of columns interacting in one plane can be considered to act as a stabilizing system.

EK632

Connections subject to impact or vibration or load reversal (other than that due solely to wind action) should not use bolts in clearance holes.

EK631

For non-sway frames designed on an elastic basis member forces under both vertical and horizontal loading should be determined from a linear elastic analysis of the whole frame.

EK630

Shear buckling resistance may conveniently be improved by dividing the web into a series of panels by using intermediate vertical stiffeners.

EK629

Shear buckling occurs largely as a result of the compressive stresses acting diagonally within the web.

EK628

Although the theory of the elastic stability of perfect pin-ended struts, sometimes referred to as the Euler theory, provides some insight into the behaviour of slender compression members, it omits […]

EK627

The design strength: The characteristic strength divided by the appropriate partial safety factor for the material.

EK626

The design load: The characteristic load multiplied by the relevant partial factor.

EK625

Partial safety factors: The factors applied to characteristic loads, and properties of materials to take account of the probability of the loads being exceeded and the assessed design strength not […]

EK624

The characteristic strength of a material: The specific strength below which not more than a small percentage (typically 5%) of the results of tests may be expected to fall.

EK623

Characteristic loads: Those loads which have an acceptably small probability of not being exceeded during the lifetime of the structure.

EK622

The serviceability limit state: Loss of utility and/or requirement for remedial action.

EK621

The ultimate limit state: Inability to sustain any increase in load.

EK620

A limit state: A condition beyond which the structure would become less than completely fit for its intended use.

EK619

In structures subject to a very large number of cycles of fluctuating load, typically at least 100000 load applications, failure may occur by the continued growth of cracks in the […]

EK617

When it is apparent that there may be a loss of friction in slip-critical bolted connection (which occurs in some type of brackets and hangers subject to tension and shear) […]

EK616

Design of slip-critical bolted connection assumes that the fastener, under high initial tensioning, develops frictional resistance between the connected parts, preventing slippage despite external load.

EK615

High-strength bolts in slip-critical joints may share the load with welds on the same connection interface if the bolts are fully tightened before the welds are made.

EK614

Bolts or high-strength bolts in bearing-type connections should not be considered as sharing the load with welds. If welds are used, they should be designed to carry the load in […]

EK613

A rule used by some designers that has proved satisfactory is to design the brace for 2% of the axial load of columns, or 2% of the total compressive stress […]

EK612

The principal function of a brace is to provide a node in the buckled configuration.

EK611

For an ideally straight, exactly concentrically loaded beam or column, only a small force may be needed from an intermediate brace to reduce the unbraced length of a column or […]

EK610

All building framing affected by overhead cranes should be braced for the thrusts induced by sidesway and longitudinal motions of the cranes. Bracing used for wind or erection may be […]

EK609

Because wind may blow from any direction, the building also must be braced for the wind load on the gables. This bracing becomes less important as the building increases in […]

EK608

A common assumption in wind distribution for the type of light mill building is that the windward columns take a large share of the load acting on the side of […]

EK607

The crane girder must be designed as laterally unsupported beam carrying vertical and horizontal load at the level of the topflange.

EK606

Plastic moments obtained by different loading systems cannot be combined, i.e. the plastic moment calculated for a given set of loads is only valid for that loading condition.

EK605

If no resistance is set up against deformation in the body, then it isknown as a mechanism.

EK604

When a system of loads is applied to an elastic body, it will deform and will show a resistance against deformation. Such a body is known as a structure.

EK603

Plastic moment condition: The bending moment at any section of thestructure should not be more than the fully plastic moment of the section.

EK602

Mechanism condition: The ultimate or collapse load is reached when amechanism is formed. The number of plastic hinges developed should bejust sufficient to form a mechanism.

EK601

The cross section is not capable of resisting any additional moment but may maintain this moment for some amount of rotation in which case it acts like a plastic hinge.

EK600

The ratio of the plastic moment to the yield moment is known as theshape factor since it depends on the shape of the cross section.

EK599

Plastic analysis is based on the idealization of the stress-strain curve aselastic-perfectly-plastic. It is further assumed that the width-thickness ratio of plate elements is small so that local buckling does […]

EK598

The effective column length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

EK597

Since it is impossible to quantify the variations in geometric imperfections, accidental eccentricity, residual stresses and material properties, it is impossible to calculate with certainty, the greatest reduction in strength […]

EK596

Horizontal stiffeners are generally not provided individually. They are used in addition to vertical stiffeners, which are provided close to the support to increase the bearing resistance and to improve […]