Stress Strain relationship for concrete and Stress Strain relationship for steel

Learn : Stress Strain relationship for concrete, Stress Strain relationship for steel,Design Strength Values for Steel Design Stresses at Specified Strains. fe 415 and fe 500

Stress Strain relationship for concrete and Stress Strain relationship for steel

Stress Strain relationship for concrete

Stress Strain relationship for concrete : The experimental or actual stress strain curve for concrete is very difficult to use in design Therefore, IS code 456:2000 has simplified or idealized it as shown in Fig. 4.1.

relationship between the stress-strain distribution in concrete
relationship between the stress-strain distribution in concrete
  • For design purpose, the compressive strength of concrete in the structure in taken as 0.67 times the characteristic strength. The 0.67 factor is introduced to account for the difference in the strength indicated by a cube test and the strength of concrete in actual structure.
  • The partial safety factor (rmc), equal to 1.5 is applied in addition to this 0.67 factor.
  • The initial portion of the curve is parabolic. After a strain of 0.002 (0.2%), the stress becomes constant with increasing load, until a strain of 0.0035 is reached and here the concrete is assumed to have failed.

Stress Strain relationship for steel

Stress Strain relationship for steel :  The stress-strain curve for mild steel, Fe 415 and Fe 500 are shown in Fig. 4.2 and 4.3.

stress strain curve for mild steel
stress strain curve for mild steel
stress-strain-curve-for-high-strength-deformed-bars
stress-strain-curve-for-high-strength-deformed-bars

For mild steel, the value of characteristic stress is taken as yield stress and the design curve is obtained after applying a factor of safety of 1.15 to yield stress. The design stress for steel is equal to \[\frac {f_{y}}{1.15}\] i.e., 0.87 fy. For high strength bars (Fe 415 and Fe 500), the yield point is not distinct, hence yield stress is taken as 0.2 percent proof stress and factor of safety is applied to it.

            Design Strength Values for Steel

(i)        For mild steel \[f_{d}=\frac{f_{y}}{1.15}=0.87f_{y}\]

and  \[(f_{y}=250 N/mm^{2}) f_{d}=0.87\times250=217.5 N/mm^{2}\]

(ii)       For Fe 415, \[f_{d}=0.87\times415=361N/mm^{2}\]

(iii)     For Fe 500, \[f_{d}=0.87\times500=435N/mm^{2}\].

TABLE 4.1. Design Stresses at Specified Strains.
Fe 500 steel : \[f_{y}=500(N/mm^{2})\] Fe 415 steel : \[f_{y}=415N/mm^{2}\]
Strain Stress (N/mm2) Strain Stress (N/mm2)
0.00174 347.8 0.00144 288.7
0.00195 396.6 0.00163 306.7
0.00226 391.3 0.00192 324.8
0.00277 413.0 0.00241 342.8
0.00312 423.9 0.00276 351.8
0.00417 434.8 0.00380 360.9

(a) Fe 500 steel                                                                   (b) Fe 415 steel

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