2. Loss of prestressing

Values ​​of the initial pre-stress remain σsp not remain constant, but decreases over time due to inevitable losses caused by physical and mechanical properties of materials you , manufacturing technology, the level of compression of the concrete. Distinguish first loss occurring during manu been compiled and compressed concrete - σlos1 and second loss occurring after crimping concrete - σlos2.

Losses can occur for the following reasons:

1. Losses from stress relaxation at constant fixture tsroiskhodyat its length stretched on supports state. These losses depend on the type of reinforcement and the method of its tension.

Under mechanical tension method:

high-strength wire and cables:

reinforcement bars:

The electrothermal method of tension:

high-strength wire and cables:

reinforcement bars:

2. Σ2 loss of temperature drop, i.e. temperature difference in the stretched over and stops the valve device which receives the tensile force during heating of the concrete. These losses depend on the concrete class design and manufacturing technology:

Concrete class B15 ... B40: σ2 = 1.25 • Δt;

Concrete classes B45 and above σ2 = 1.0 • Δt,

where Δt-temperature difference between the heated valve and fixed stops perceiving tension force, ° C;

in the absence of accurate data taken Δt = 65 ° C.

3. The losses on the deformation of anchors disposed at tensioners. These losses depend on the method of prestressing anchors and design:

with mechanical valves in the process of pulling the stops:

where Δl = 2 mm - when compressing opresovannyh washers or creasing heads and landed - the displacement rods in inventory terminals; d - diameter of reinforcement, mm;

l-distance between pinning points tensioned reinforcement, mm;

the electrothermal method of tension reinforcement at stops loss of the deformations of anchors in calculation does not take into account, as they are taken into account when determining the elongation valves on heating, ie in this case, σ3 = 0;

with post-tensioning:

where Δl1 = 1 mm - compression washers or spacers disposed between the anchor and the concrete structure and Δl2 = 1 mm deformation anchors glass type pad with stoppers, anchor nuts and grabs; l-length of the pull rod (element length), mm.

4. Σ4 loss from friction fittings. These losses are determined depending on the method of prestressing:

• pulling on concrete reinforcement loss from friction against the walls of the channels or the surface of the concrete structures are defined by the formula

by pulling on the supports loss from friction fittings on envelopes devices defined by the formula

where e - base of natural logarithms;

ω-coefficient, depending on the type of surface sion on Table 6 SNIP 2.03.01-84 "Concrete and reinforced concrete con-struction";

δ-coefficient, depending on the species and the fittings ry species surface Table 6 SNIP 2.03.01-84 "Concrete and same-lezobetonnye design";

χ - length of the section of the tensioner to the calculated cross section of , m;

θ-total rotation angle valves, rad.;

σ_sp-taken without previously incurred losses.

5. Σ5 loss from deformation steel mold for fastening reinforcement on the palm shape. These losses depend on the technology and the design of forms:

reinforcement by pulling jack:

pulling fittings winder Elektroterm-mechanical process:

where Δl-stops closer to the line of action of compression force, determined from the calculation of the deformation shape

l-distance between the outer edges of the stops;

in the absence of data on manufacturing technology and design forms σ5 = 30 MPa;

the electrothermal method tension σ5 = 0.

6. Loss of σ6 bystronatekayuschey creep develop during compression concrete tendon pulling on the supports. The magnitude of these losses depends on the strength of concrete at the time of compression, the stress level of compression and hardening conditions. Hardening concrete in vivo:

where the coefficients

In this case the following restrictions: α≤ 0.8 и 1.1≤β≤2.5. Compression stress in concrete σbr defined at the center of gravity of prestressing steel and Asp A'sp with lossy σ1 - σ5. Hardening of concrete under thermal processing the value multiplied by a factor 0.85.

Loss σ1 - σ6 belong to the first loss in tension reinforcement at the stops. And with post-tensioning can be shown only loss σ3 and σ4. Thus, the magnitude of the first casualties will be:

by pulling on the valve stops

with post-tensioning

Preliminary stress in prestressing reinforcement after the occurrence of the first casualties:

7. Σ7 loss of stress relaxation in the reinforcement by pulling her onto concrete accepted the same as pulling the stops on σ1.

8. Loss σ8, shrinkage of concrete and the corresponding reduction element depends on the type of concrete, prestressing method and conditions of hardening concrete. The values ​​given in Table. 8.1.

9. Σ9 loss of concrete creep. These losses are due to the shortening of the element of a long-acting compression efforts. The magnitude of these losses depends on the strength of concrete at the time of compression, compression stress level, type and conditions of hardening concrete. For heavy and light concrete with a dense aggregate value of these losses is determined as follows:

• If the voltage level , the concrete experiences and linear creep:

Table 8.1

Loss of stress in the prestressing steel from the shrinkage of concrete, Mp

Typeofconcrete	tensionreinforcement
	onthesupports		onconcrete
	Hardeninginvivo	Heat treatment at atmospheric pressure	Regardless of the curing conditions
Heavy classes:             At 35 and below             In 40             At 45 andabove	40 50 60	35 40 50	30 35 40
Lightweight, with a fine aggregate: dense porous	50 70	45 60	40 50
fine-grained,
A groupofclasses
At 35 andbelow	52	45.5	40
At 40 andabove	65	52	40
B	60	75	50
In	40	40	40

If the voltage level it has a non-linear creep and

σbr where is defined the same as in detecting loss of creep, but given the manifestation of loss σ1 - σ6; hardening in vivo coefficient α = 1, with a heat treatment at atmospheric pressure - α = 0.85.

For lightweight concrete with porous aggregates values ​​are multiplied by a factor equal to 1.2. For fine-grained concrete groups A and B are introduced multiplying factors, respectively, 1.3 and 1.5, and for group B - the amount of losses is determined by the coefficient α = 0.85

10. Σ10 losses from collapse of the concrete under the turns of the spiral or ring fittings. These losses account for only elements with post-tensioning in construction with an outer diameter of up to 3 m dexl Their value is determined by the formula:

11. Σ11 loss of compression deformation of joints between prefabricated blocks. These losses are determined by post-tensioning in structures consisting of individual units according to the formula:

where n - the number of seams along the length of tensioned reinforcement;

l-deformation joints, equal to 0.3 mm at every seam, filled with concrete, and 0.5 mm at jointing dry;

1 - length tensioned reinforcement, mm.

Lossσ₇-σ₁₁ and relate to the second loss. At the same time pulling the valve on the supports may be expressed only loss σ₈ and σ_9.

Thus, the magnitude of the second loss will be:

by pulling the valve stops at:

with post-tensioning

The total loss in any method of pre-stressing will be:

Preliminary stress in pre-stressing reinforcement after the onset of the losses will be:

In non-prestressed reinforcement elements under the influence of joint deformities occur with concrete initial compressive stresses. When compressing the concrete they are numerically equal losses from creep, i.e.σs = σ6.

And before uploading designs added to them losses from shrinkage and creep, i.e.

3. Stresses in the concrete at a reduction

When designing the construction of pre-stressed tension should be considered in the concrete resulting from the stresses in it at various stages of compression of the structure.

The amount of force preliminary deformation of concrete is defined as the resultant of forces across the longitudinal reinforcement by the formula

Where - pre-stress in pre-stressing steel, respectively taking into account the losses incurred;

- Voltage fixture respectively non-prestressedAs and A 'caused by shrinkage and creep of concrete - a precision factor tension reinforcement.

Eccentricity of application of the resultant compression force relative to the center of gravity of the reduced section will be:

Where - the distance between the axis passing through the center of gravity of the reduced section, and lines of action efforts in the relevant rebars (wires) (Fig. 8.1).

Force distribution in the cross section element under eccentric compression:

1 - line passing through the center of gravity of the reduced section

Pre-stress in the concrete is defined as woo tic body given by the geometric characteristics of the cross section. Reduced cross-section includes concrete cross section and the cross section across the longitudinal reinforcement, replaced the equivalent cross-sectional area of the concrete.

Normal stresses in the concrete efforts of compression generally defined as for eccentrically compressed elastic body on the cross section according to the formula given

Whereyi - the distance from the center of gravity of the reduced section to the fiber, which is determined by the value σbr

Ared - reduced section area;

Ired - moment of inertia of the reduced section;

Mg - bending moment due to dead weight.

Quiz:

1. What is pre-stressed concrete?

2. What is the loss of pre-stressing concrete efforts to transfer tension concrete (first loss)?

3. What is the loss of pre-stressing concrete after transferring force to the concrete (second loss)?

Theme 10 Strength calculation bent elements for normal sections

1. Understanding bending elements

2. Derivation of equations for the calculation of elements of arbitrary profile

3. Calculation of the elements of rectangular cross section with a single armature

1. Understanding bending elements

In construction practice widely used concrete same elements,the most common of which are the slabs and beams.

Plates called concrete structures in which the thickness is much less than the other two dimensions - span and Shea cross-sectional widths. Plates perform continuous, and ribbed , according to the method of production - teams , monolith and precast- monolithic (Fig. 9.1). National slabs poured as the relatively small size and large size such as to cover industrial buildings with enlarged mesh Colon ( see lecture number 36).

Flexural concrete elements

and prefabricated overlap b - solid joists, 1 - stove, 2 – beam.

Slabs reinforced with welded wire mesh mainly whose armature in one direction - working, and the other distribution (assembly). Working fittings perceives tensile forces arising from the bending moment. Distribution rods provide design position during concreting workers rods perceive not deductible calculation effort from concrete shrinkage and temperature changes, and the action of local loads - distribute them over a larger area. Stoves in two directions, reinforcing mesh, having rods working in both directions. The most common solutions for the reinforcement of concrete slabs are presented schematically in Fig. 9.2 .

Beam - the design for which the length is much more the other two dimensions (b <l> h). Beams serve as supports for the boards are the foundation slab. Sectional beams are rectangular, tee, flange beams, trapezoidal, with cross and other profiles. By the number of spans and character bearing beams can be single span the exposed, extremely single-span clamped at one or both poles, uncut and multi-span cantilever.

Selecting the type and size of precast beams are produced in accordance with the nomenclature and standardized sizes of precast concrete products and designs. Examples of precast concrete beams are shown in Fig. 9.3, 6.

Beams reinforced with longitudinal and transverse reinforcement, while knitted frames - and bent. Working reinforcement beams located in the tension zone in accordance with the bending moment. Transverse vertical rods or straps tie between a stretched and compressed zone beams and perceive shear and tensile stresses principal.

In precast beams along with T-section welded frame in the ribs for reinforcement welded wire mesh shelves are used. Scheme reinforced concrete beams are shown in Fig. 9.3.

Flexural concrete elements used as a conventional reinforced and pre-stressed reinforcement. Used for the manufacture of hard, fine-grained and lightweight concrete classes in 15 ... In 60.

Pairing precast elements interconnected issues weld fittings or metal fixings followed by concrete embedment.

2. Derivation of equations for the calculation of elements of arbitrary profile

Exhaustion of the bearing capacity of flexural members can occur as the bending moment M at low or zero shear force curve Q (normal to the longitudinal axis of the cross-section 1-1), and 100 of the shear force Q at a relatively small value of the moment M (oblique section) (Fig. 9.4).

The Calculation of flexural elements:

1 - normal section 1-1, for which there was a destruction element, 2, 3 -, respectively, normal and oblique crack 4 - Working longitudinal reinforcement.

The destruction of the normal cross-section may occur in one of two cases, due to the mechanical properties and the amount of working reinforcement elements located in the cross section . Thus, if the amount of reinforcement does not exceed a certain value (normally reinforced beam ) in the area of ​​the greatest moment of destruction begins with strength tensile reinforcement in the tension zone cracks develop to a considerable height element deflections sharply increasing, and only then crushed concrete uncracked ( step III, in case I).

If the same amount of reinforcement is more than a certain value, the destruction begins with uncracked concrete. Stress in the tension reinforcement is not reach the limit values ​​(tensile yield strength), fittings will not be used fully.

When a small amount of reinforcement with the advent of the first crack, fittings immediately broken and destroyed as a concrete element.

In accordance with the above causes exhaustion carrying capacity, there are two cases for calculating the flexural elements normal sections: Case 1, when the compressed concrete and tensioned reinforcement reached the limit values ​​of voltages, ie calculated resistance Rb and Rs 2 case when cracked concrete limit is reached compression resistance (Rb), and tensioned reinforcement instead of Rs acts less stress σs.

Boundary position between the cases 1 and 2 is set depending upon the relative height of the compressed zone. value at which the simultaneous exhaustion of bearing capacity of concrete uncracked and tensile reinforcement designate If ξ <ξR-case 1, if ξ>ξR that case 2. The boundary value of the relative height of the compressed zone is determined by the empirical formula obtained on the basis of statistical data processing multiple pilot studies depending on ξRσs

Where - characteristics of uncracked concrete.

Here α-coefficient taken equal for concrete:

Heavy 0.85

fine:

groups:

A 0.80;

B and 0.75;

light, porous ... 0.80;

- the ultimate stress in the reinforcement of the compressed zone, when the received equal to 400 MPa, and for the elements of heavy, fine-grained and light concretes, if taken into account - to 500 MPa.

- ultimate stress in the reinforcement tension zone, MPa taken for fittings classes:

Here Rs - calculated resistance tensile reinforcement into account all relevant factors for reinforcement, except

- pre-stress in the reinforcement with all the losses and accuracy factor of tension

- combined with mechanical methods of pre-stressing reinforcement classes

with other methods of pre-stressing reinforcement classes A-IV, AV, A-VI, as well as fittings for classes B-II, Bp-II,

K-7 and K-19 in all methods of pre-stressing reinforcement value σsp = 0.

R values ​​for physical reinforcement yield strength for all types of concrete are given in the references.

Strength calculation of the normal sections bent elements is to determine the size of the cross section of the element and the cross sectional area of ​​the tension reinforcement work, commuting ¬ guarantee reliable performance of reinforced concrete structures in the stage of manufacturing, transportation and installation, and for a specified period of service buildings.

Strength of the normal sections calculated efforts derived from the calculation of reinforced concrete structures on the estimated impact of static or dynamic loads. Strength calculation bent elements for normal sections relates to the calculation of the first group of limit states. The basis of calculating the strength of the cross sections on the following main assumptions:

internal forces in the billing section of an element are to stage its destruction;

considered section passing through the fracture in cracked concrete, concrete tensile resistance is ignored;

resistance of concrete compressive stresses are equal to Rb, and take a rectangular stress distribution;

tensile stresses in the reinforcement does not take more than its calculated resistance Rs, compression - no more than the design resistance Rsc.

Determination of stress in normal sections of elements is a statically indeterminate problem, because the required four values ​​(A, Rb, As, Rs), and you can use only two static equation:

Therefore, the calculation of the normal sections performed on the assumption that we are given three of the four unknowns

-