Structural materials Characteristics, testing, strength evaluation

Transcription

1 Budapest University of Technology and Economics Department of Mechanics and Materials of Structures English courses General course /2013 Fundamentals of Structures BMEEPSTG201 Lecture no. 3: Structural materials Characteristics, testing, strength evaluation FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 1

2 Introduction Structural materials are used to construct the loadbearing structural part of building constructions. Loadbearing structures of buildings should safely support loads acting on the structure (without demage, rupture, loss of stability, falling over or down), and transmit loads to the subsoil under the building. Their most important characteristic is having adequate strength. Strength is the greatest force per unit area that the material cab bear without demage, rupture. Tensile strength, compression strength and shear strength can be distinguished, according to the way of actuation the force is acting on to the cross-section of the investigated member. Considering a cross-section of a short linear member, the above strengths can be determined approximately as indicated on the figure: FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 2

3 1. General requirements of structural materials structural requirements non-structural requirements strength space limitation tensile strength (f t ) thermal insulation compression strength (f c ) sound insulation shear strength (f τ ) economicity, prize deformability elastic, elastic-plastic, plastic, brittle behavior ultimate deformation density, specific weight (γ) fire resistance durability, resistance to corrosion remodelation possibilities FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 3

4 2. Mechanical characteristics of some structural materials Materials Strength Deformability f d /γ ratio compression tension at σ=f d at rupture (kn/m 2 )/(kn/m 3 )= N/mm 2 mm/m=%o =m Sun-dried brick 0,2 0 Cer.ic brick+lime m. 0, , Cer. brick+cement m. 0,8-3,5 0 0,8 4 Natural stone , Concrete light normal , ,5-3,5 320 high strength Timber (parallel to fibre direction) Iron Steel mild high strength steel Reinforced concrete see concrete see concrete 1200 FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 4

5 (Continuation) Materials Strength Deformability f d /γ ratio compression tension at σ=f d at rupture (kn/m 2 )/(kn/m 3 )= N/mm 2 mm/m=%o =m Glas very small Aluminium Fibre-reinforced plastics Numerical example for better understanding G man 0,8 kn= 800 N A palm 100x100 = mm 2 G σ soil man 800 = 0, 1N/mm 2 Asoil Compare this stress You can feel with material strengths indicated above! FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 5

6 1. Uniaxial stress-strain relationships of structural materials Definitions: Stress = σ = force per unit area = A F (N/mm 2 ) Stress at rupture= strength (compression or tensile strength according to the direction of F) Strain = ε = specific deformation = alongation or contraction Δl = length l Plastic behaviour: the material deforms under compression or tension without stress increment Characteristic mechanical behaviours in uniaxial stress state FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 6

7 elastic rigid-plastic elastic-plastic nonlinear Hook's law describes the linear elastic mechanical behaviour: σ = E ε where E: modulus of elasticity (N/mm 2 ) Definition of E: the value of the stress to be applied to double (or in case of compression to halve) the length of the member (ε=1) FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 7

8 Characteristic σ-ε relationships of some important structural materials: timber steel concrete Idealized stress-strain relationships: timber steel concrete FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 8

9 Test specimens used for uniaxial tests timber steel concrete FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 9

10 Static bending test of a timber specimen Tension test of steel specimen FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 10

11 Mechanical behavior of the tested materials Timber Strength perpendicular to grains is different (very low). Linear elastic behavior. Strength is similar to compression strength of concrete. Steel After linear elastic behavior yield produces great plastic deformation. The same strength in compression or tension. The strength is approximately 10 times greater than that of timber. Concrete Compression and tensile strength is very different. After short linear behavior non-linear σ-ε curve can be observed. Ultimate deformation is much smaller than that of steel. Brickwork Negligible tensile strength. The strength of brickwork is much smaller, than that of ceramic bricks. Compression strength is at about by one order of magnitude smaller than that of concrete. FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 11

12 2. Strength as probability variable 2.1 Statistical strength data no. of occurance relative occurence A n A=1 strength f (N/mm 2 ) strength Strength distribution diagram Density function of strength (histogram) distribution A n The probability of not exceeding f nom = = A n A FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 12

13 2.2 Statistical evaluation of test results (Statistical strength evaluation9 Characteristics of the strength distribution Σf Mean value: f m = i n n: number of test data (min 10, if qualification is based on unknown scatter) 2 Σ(fi fm ) Scatter: s= n 1 Threshold value (characteristic or nominal value): f k = f m ts where t is the so called Student factor, which, for n=10 and 5% risk is t=1,79 (5% threshold value: the probability of the occurence of a strength value smaller than f k is 5%) FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 13

14 Relation of characteristic and design value relative occurance A n f k f d f k f =f m strength (N/mm 2 ) Design value: f d = γ m The probability of f d not being exceeded is 0,1% γ m for some important structural materials 1,15 for reinforcement (steel in reinforced concrete) 1,3 for timber 1,5 for concrete FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 14

15 Example: test data evaluation of a timber test specimen subjected to axial compression in direction of the grains. Specimen data: 2x2x3 cm timber No. Cross-section Rupture load Rupture strength A N u f u f ui - f m (f ui - f m ) 2 mmxmm kn N/mm 2 N/mm 2 N 2 /mm x 19,8 26,7 67,42 1,62 2, x ,50 1,70 2, ,7 x 19,2 24,5 64,77-1,03 1, x 19,6 25,4 64,79-1,01 1, x 20 28,2 70,50 4,70 22, x 20,6 24,8 60,19-5,61 31, x 20 27,0 67,50 1,70 2, ,7 x 20,5 25,3 59,62-6,18 38, ,6 x 19,3 26,0 68,73 2,93 8, x 20 26,7 66,75 0,95 0,90 Mean value of the rupture strength: 2 ui m ) Σ( f f = 111,71 FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 15

16 Σfu 657,77 f m = = = 65,8 N/mm 2 n 10 The scatter: 2 Σ(fi fm ) 111,71 s= = = 3, 52 N/mm 2 n 1 9 The characteristic compression strength: f k = f m - ts= 65,8 1,79 3,52 = 59,5 N/mm 2 for n= 10 and 5% risc the Student factor: t=1,79 Design compression strength: f f d = k 59,5 = = 45, 76 N/mm 2 γ m 1,3 the safety factor for timber: γ m = 1,3 FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 16

17 TESTING OF PREFABRICATED REINFORCED CONCRETE BEAMS IN.2005 IN THE LABORATORY OF THE DEPARTMENT OF STRENGTH OF MATERIALS AND STRUCTURES FUNDAMENTALS OF STRUCTURES STRUCTURAL MATERIALS page 17

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