混凝土和钢的应力-应变关系外文翻译资料

Stress-Strain Relationships for Concrete and Steel

2.1CONCRETE

2.1.1 Uniaxial Stress Behavior .

Under practical conditions concrete is seldom stressed in one direction only (uniaxial stress), since in most structural situations the concrete is stressed simultaneously in a number of directions. Nevertheless, an assumed uniaxial stress condition can be justified in many cases.

Compressive Stress Behavior

The compressive strength of concrete is usually obtained from cylinders with a height to diameter ratio of 2. The cylinders are loaded longitudinally at a slow strain rate to reach maximum stress in 2 or 3 minutes. The normal .standard cylinder is 12 in (305 mm) high by 6 in (152 mm) diameter and the compressive strength attained at 28 days usually ranges between 2000 and 8000 psi (13.8 to 55.2 N/mm²). Smaller size cylinders, or cubes, are also used, particularly for production control, and the compressive strength of these units is higher. With appropriate conversion factors obtained from tests, the results from such specimens can be converted into equivalent standard cylinder

strength values.

Figure 2.1 presents typical stress-strain curves obtained from concrete cylinders loaded in uniaxial compression in a test conducted over several minutes. The curves are almost-linear up to aboujjine-half the compressive strength. The peak of the curve for high-strength cracrete is relatively sharp, but for low-strength conprete the curve has^ JaLtop. The strain at the maximum stress is approximately 0.002. At higher strains, after the maximum stress is reached, stress can still be carried even though cracks parallel to the direction of the loading become visible in the concrete. Concrete tested in flexible testing machines sometimes fails explosively because the concrete

0 0.001 0.002 0.003 0.004

Concrete strain

Fig. 2.1. Stress-strain curves for concrete cylinders loaded in uniaxial compression.

cannot absorb the release in strain energy from the testing machine when the load decreases after maximum stress. A stiff testing machine is necessary to trace the full extent of the descending branch of the stress-strain curve.

The modulus of elasticity for concrete E_c may be taken as².¹

E_c = w¹⁵33radic;fcPsi (2.1)

(1 psi = 0.00689 N/mm²), where w is the density of concrete in pounds per cubic foot (1 lb/ft³ = 16.02 kg/m³) and is the compressive cylinder strength in psi. Equation 2.1，which applies for values of w between 90 and 155 Ib/ft³, was determined by Pauw^{2 2} from short-term loading tests; it gives the secant modulus at a stress of approximately 0.5. For normal weight concrete, E_c may be considered to be 57,000radic;fcpsi or 4730radic;fcN/mm².

Tests by Riisch^2,3 have indicated that the shape of the stress-strain curve before maximum stress depends on the strength of the concrete (see Fig. 2.2). However, a widely used approximation for the shape of the stress-strain curve before maximum stress is a second-degree parabola. For example, the often quoted stress-strain curve due to Hognestad^{2 4} is shown in Fig. 2.3, where f' is the maximum stress reached in the concrete. The extent of falling branch behavior adopted depends on the limit of useful concrete strain assumed. This aspect is further discussed in Chapters 3 and 6 with regard to calculations for the flexural strength and ultimate deformations of members. The maximum compressive stress reached in the concrete of a flexural member fc may differ from the cylinder strength fc because of the difference in size

1.0

Strain, in/in丨mm/mm}

0 0.0005 0.001 0.0015 0.002 0.0025

0

0.25

0.50

0.75

FIG.2.2 Relationship between the stress to strength ratio and strain for concrete of different strengths；

2.3 Idealized stress-strain curve for concrete in uniaxial compression

and shape of the compressed concrete. The strength of concrete in members with flexure is treated at greater length in Chapter 3.

When the load is applied at a fast strain rate, both the modulus of elasticity and the strength of the concrete increase. For example, it has been reported²⁵ that for a strain rate of 0.01/sec the concrete strength may be increased as much as 17%.

Repeated high-intensity compressive loading produces a pronounced hysteresis effect in the stress-strain curve. Figure 24 gives test data obtained

Strain, in/in (mm/mm)

Fig. 2.4. Stress-strain curves for concrete cylinder with high-intensity repeated axial compressive cyclic loading.^{2 6}

by Sinha, Gerstle, and Tulin²*⁶ for slow strain rates. Their tests, and those of Karsan and Jirsa,²*⁷ indicated that the envelope curve was almost identical to the curve obtained from a single continuous load application.

Riisch,².⁸ who has conducted long-term loading tests on unconfined concrete, has found that the sustained load compressive strength is approximately 80 % of the short-term strength, where the short-term strength is the strength of an identically old and identically cast specimen that is loaded to failure over a 10-minute period when the specimen under sustained load has collapsed. In practice, concrete strengths considered in the design of structures are usually based on the anticipated short-term strength at 28 days. The strength reduction due to long-term loading will be at least partly offset by the property of concrete to reach a higher strength at greater ages. Also, the capacity reduction factor cp is low when the compressive strength of concrete is critical. Creep strains due to long-term lo

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