STRUCTURAL ANALYSIS. PSDS s.r.o. IČ: TRABANTSKÁ 673/18, PRAHA 9. for building permit. March 2012 NUMBER OF PAGES 15

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1 2012 CONSTRUCTION DEGREE for building permit STRUCTURAL ANALYSIS March 2012 PERSON RESPONSIBLE Ing. Jiří Surovec NUMBER OF PAGES 15 PSDS s.r.o. IČ: TRABANTSKÁ 673/18, PRAHA 9 ( GSM: * psds@psds.cz

2 CONTENT 1. Materials and works cited Identification data Structure description Structural analysis Load Load on roads Load of railway transport Material characteristics Design procedure MKP analysis (analysis by means of the method of finite elements) Bearing capacity of the extended belt Results Deformation Tension Extended belt assessment Assembly schedule Conclusion cable trench cover plate PVC and PE pipes Page 2/15

1. MATERIALS AND WORKS CITED [1] Drawing documentation of the pit's shape [2] ČSN EN 124: Gully tops and manhole tops for vehicular and pedestrian areas [3] ČSN EN 1990: Basis of structural design

3 1. MATERIALS AND WORKS CITED [1] Drawing documentation of the pit's shape [2] ČSN EN 124: Gully tops and manhole tops for vehicular and pedestrian areas [3] ČSN EN 1990: Basis of structural design [4] ČSN EN : Traffic loads on bridges [5] ČSN : Subsoil under shallow foundations [6] Decree SŽDC S3 "Railways superstructure" [7] ČSN EN 10080: Steel for the reinforcement of concrete 2. IDENTIFICATION DATA TYPE OF CELLAR CLIENT CWS s.r.o. Tovární 1378/ Ústí nad Labem CONTRACTOR Ing. Jiří Surovec PSDS s.r.o. IČ: Trabantská 673/ Praha 9 PERSON RESPONSIBLE Ing. Jiří Surovec, Ph.D. Authorisation: authorised technician for statics and dynamics of constructions and for transportation constructions (AO ) cable trench cover plate PVC and PE pipes Page 3/15

4 3. STRUCTURE DESCRIPTION The subject of the assessment is the polyethylene cable cellar with external dimensions at the bottom of mm and the base height of 800 mm. The height of the pit can be adjusted by means of additional units with height of 280 mm up to the total height of 1920 mm. The cellar is designed to be installed bellow ground, so the loads are appropriate for roads class A to D in compliance with ČSN EN 124 and for railway transport for the load model 71 in compliance with ČSN EN The walls of the cellar have constant width of 12 mm and in the mm grid are reinforced by ribs with thickness of 12.5 to 14 mm. The ribs are reinforced towards the upper frame bearing the cover. The cellar does not have a bottom. The forces from the cover load will not be primarily transferred via the braces of the cellar walls, but by the bearing concrete ring. Fig STRUCTURAL ANALYSIS 4.1. LOAD LOAD ON ROADS In compliance with [2] four types of loads are considered: A 15 for surfaces used exclusively by pedestrians and cyclists B 125 for sidewalks, pedestrian zones and similar areas, zones for pulling over and parking of cars, even in floors C 250 for gratings placed in the area of drainage strips of roads D 400 for roads, hard shoulders and parking areas accessible for all vehicles cable trench cover plate PVC and PE pipes Page 4/15

5 Load as specified by the requirements of the given class acts on the surface of the road in a circular area with 250 mm in diameter. This load is in compliance with article 4.3.6(2) of standard [4] distributed with a slope of 45 to the level of the road base course. In the base course, the load is further distributed with a slope of 30 from the perpendicular (article 4.9.1(1), note 2). Due to the distribution the uniformly distributed surface load from concentrated load decreases with depth. To this uniformly distributed load a vertical load of the road layers is added (γ concrete = 25.0kN/m 3, γ earth = 18.0kN/m 3 ). The conversion of the vertical to the horizontal load was performed via the coefficient of active earth pressure according to Coulomb with well graded gravel as backfill material (ϕ = 44 ) K A = (1 sin ϕ) / (1 + sin ϕ) = 0.18 The resulting pressures acting on one side of the pitch shell are shown in Table 4.1. depth Ø A p vehicle g earth p total f total m m m2 kpa kpa kpa kpa 0,4 1,05 0,87 461,95 10,00 471,95 85,03 0,5 1,17 1,07 374,95 11,80 386,75 69,68 0,6 1,28 1,29 310,39 13,60 323,99 58,38 0,7 1,40 1,53 261,18 15,40 276,58 49,83 0,8 1,51 1,80 222,81 17,20 240,01 43,24 0,9 1,63 2,08 192,31 19,00 211,31 38,07 1,0 1,74 2,39 167,67 20,80 188,47 33,96 1,1 1,86 2,71 147,48 22,60 170,08 30,65 1,2 1,97 3,06 130,73 24,40 155,13 27,95 1,3 2,09 3,43 116,68 26,20 142,88 25,74 Tab Earth pressure up to the load class D LOAD OF RAILWAY TRANSPORT -1,20 0,0 50,0 100,0-1,40 horizontal tension[kpa] Please note that in compliance with Decree SŽDC S3 the structures, facilities or parts thereof cannot interfere with the railway bedding and with the working area of mechanical devices defined in the railway stations and shunts (with the exception of switch head) by the distance of 2.2 m from the railway axis (in narrow space the distance of 2.05 m is permissible, if the length of the base does not exceed 2.0 m) and in the open track up to the outmost switch by the distance of 2.35 m from the railway axis. For the structural analysis the load model of 71 is used supposing the 1st class track (α = 1.21). Due to long distance of the pitch from the acting load, orthogonality of the acting force and the load deduced, but also due to the flexible base and geometric attenuation, the dynamic coefficient was established to be equal to depth [m] -0,40-0,60-0,80-1,00 Distribution of the load perpendicularly to the railway line was in compliance with [6] estimated in the gravel ballast in the ration of 4:1; in lower structural levels the distribution of the load with a slope of 30 from the perpendicular was estimated. The height of the railway bedding under cable trench cover plate PVC and PE pipes Page 5/15

the upper edge of the sleeper was estimated as 400 mm at minimum, parallel to the railway line the load was estimated as continuous. The length of the sleeper was estimated to 2.

6 the upper edge of the sleeper was estimated as 400 mm at minimum, parallel to the railway line the load was estimated as continuous. The length of the sleeper was estimated to 2.42 m, with increment of 4:1; following the height of the gravel filling the width of the loading belt in the depth of 0.4 m was estimated to ( )/4 = 2.55 m (in this case the sleeper height of 0.15 m was estimated). The width further increases with a slope of 30. Load acting on the base from the load model 71 in the depth of 0.4m (on the surface of the ground level) is defined as /( ) = kn/m 2, with increasing depth the width of the loading belt in the denominator increases with the increment of 2 tg (30 ) Δh. The horizontal load in the given depth is calculated by multiplying by the coefficient of active earth pressure K A MATERIAL CHARACTERISTICS The following main material characteristics for polyethylene HD were used: elastic modulus yield point E = 1 000MPa f t = 25MPa density γ = 10kN/m 3 material coefficient γ Μ = DESIGN PROCEDURE MKP ANALYSIS (ANALYSIS BY MEANS OF THE METHOD OF FINITE ELEMENTS) For the structural analysis the Dlubal RFEM 4.09 program was used, where a 3D wall-board model for evaluation of the pit plastic construction was used. Elements with variable width were used. The positive arch effect of the earth was neglected. Full load of the designed wall was established. The structure is established as rigid in the cover level. The pitch was modelled without the reinforcing bottom. One set of load states was designed, which was applied to the model in 12 subsequent substeps by gradual ballasting-up. Elastoplastic nonlinear analysis with consideration of the 3rd grade theory (theory of large deformations) was used. Fig Model for the load class D used cable trench cover plate PVC and PE pipes Page 6/15

7 BEARING CAPACITY OF THE EXTENDED BELT Since the Zekan system enables to create a wide range of pit dimensions, a uniform method utilising the bearing capacity of the individual ribs of the system was used for evaluation of the lower edge of the extended belts. The moment of inertia of the individual ribs was defined as cm 4, which for the yield point of 25 MPa allows for stress of 0.31 knm/rib. In total, for the rib width of 14 cm it is the characteristic value of 2.18 knm/m and design value of 1.74 knm/m RESULTS DEFORMATION Based on the development of the deformations it is obvious that the Polyethylene in the most exposed points reached the yield point, which resulted in plastic deformations. This is visible in particular based on the maximum values of the plastic deformation in Fig The yield point corresponds to the relative deformation of ε = 0.025, which corresponds to the transition of green and yellow colour. Higher values appear only in the vicinity of steel joints. However, the reason is the inaccuracy of the model, where the joints act in one point of the structure. The absolute value of the maximum shift is 55.4 mm in the middle of the walls span between the concrete collars. However, larger deformations allow for creating of an arch in the filling earth and thus substantial decrease in the stress of the cellar walls. Fig Deformation and load cable trench cover plate PVC and PE pipes Page 7/15

Fig. 4.3 - Maximum relative transformation 4.4.2.

cellar walls started to transform plastically.

8 Fig Maximum relative transformation TENSION The maximum values of tensile and compressive stress exceeded the values of the yield point stress, so the cellar walls started to transform plastically. The plastic joints are thus gradually transformed in the points of tension of steel connectors as well as in the middle of the side wall (point of the highest shifts achieved). Fig Maximum pressure stress cable trench cover plate PVC and PE pipes Page 8/15

9 Fig Maximum tensile stress EXTENDED BELT ASSESSMENT For load of 40 kn/m 2 (D class) on the suspended lower belt acting as a console with 0.18 m in length the concluded bending moment is 0.64 knm. For load of 16 kn/m 2 (B class) on the lower belt supported on both ends by the concrete ring and acting as a plain beam with 0.46 m in length the concluded bending moment is 1,69 knm. Both values do not exceed the projected value of bearing capacity of 1.74 knm/m. The crosssection is therefore sufficient. 5. ASSEMBLY SCHEDULE The Zekan cable cellars must be laid in well compact ballast bed of well graded gravel (GW) 1/8 fraction of minimum width 200 mm. The backfill must be of the same material (GW, 1/8 fraction) and must be well compacted with layers of maximum width 200 mm. The backfill will be used to the level of the bottom edge of the bearing concrete ring. The bearing ring, the height of which will change depending on the load class, fulfils bearing function for potential concentrated load in the vicinity of the cellar entry and at the same time reinforces the cellar entry. For the load class B and load model 71 its height will be at minimum 200 mm and it will be made of plain concrete. For load classes C and D its height will be 400 mm and it will be equipped with three reinforcing rods attached to the cellar structure via steel joints. In the ring there will be reinforcement along the whole circumference. However, it will be connected to the cellar structure only in points with bolted connections of the individual cellar plates. For load class A no upper bearing ring is necessary. The following concrete ring will be placed on the bottom edge of the first piece (in the depth of 800 mm), it will be 200 mm high and will be equipped with two reinforcing rods. The load class A cable trench cover plate PVC and PE pipes Page 9/15

10 is an exception. For this class the concrete ring will be placed on the bottom edge of the first adjusting belt (in the depth of 1,080 mm). In case the cellar is raised above the base height, some deeper joints will need to be equipped with another ring of reinforced concrete. For load A and B the concrete ring will be placed on the bottom edge of every third adjusting belt; for load classes C and D and load model 71 on the bottom edge of every second adjusting belt. If the lowest ring of reinforced concrete is placed at the bottom edge of the cellar, the lowest concrete ring can be replaced with steel sections. The steel sections will shore the longer walls of the cellar and will be placed equally along its length depending on their number. For load classes A and B, two shores are sufficient. For load class C and D and load model 71 four such shores are required. The steel shores will be strutted against the cellar wall by means of base plates with minimum area of 1 dm 2, so the cellar walls do not get pierced. The shore will be made of L 50 5 section or bigger appropriate section (with minimum area of 500 mm 2 ) with similar strut characteristics. The rings will be made of C20/25 concrete and their width will be at minimum 200 mm from the outer edge of reinforcing ribs. The shore will be ribbed with diameter of 12 mm made of B 500 B steel (in compliance with [7] ) and along the longer cellar wall it will be attached to the structure by means of steel joints. If the pit is placed near the railway where there is a risk of stray current, the shore needs to be welded in the horizontal rings! 6. CONCLUSION A detailed structural analysis by means of the method of finite elements was performed and it was proved that the Zekan XXL cable cellar when installed in compliance with chapter 5 conforms to the conditions appropriate for the loads for coverage of vertical structures of types A15, B 125, C 250 and D 400 in compliance with the applicable standard EN 124 and to the load model 71 in compliance with the applicable standard ČSN EN Please note that in compliance with Decree SŽDC S3 any part of the pit can be placed within the distance of 2.2 m in railway stations and shunts (in narrow space the distance of 2.05 m is permissible, if the length of the base does not exceed 2.0 m) and in the open track up to the outmost switch by the distance of 2.35 m from the railway axis. The assembly procedures proposed are applicable to cellar heights up to 1920 mm. For installation of cellars above this height please consult a structural designer. cable trench cover plate PVC and PE pipes Page 10/15

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Code No: R Set No. 1

Code No: R Set No. 1 Code No: R059210303 Set No. 1 II B.Tech I Semester Regular Examinations, November 2006 MECHANICS OF SOLIDS ( Common to Mechanical Engineering, Mechatronics, Metallurgy & Material Technology, Production