draw a neat sketch of representative stress strain curve given is IS 456 for cold worked deformed bars

To create a neat sketch of the representative stress-strain curve for cold worked deformed bars as per IS 456, it’s important to provide a description without an actual image, as I cannot directly draw. Here is how you can imagine or sketch it:

Title: Stress-Strain Curve for Cold Worked Deformed Bars

1. Axes:

   • Draw two axes:
     • The horizontal axis (x-axis) represents Strain ($\epsilon$).
     • The vertical axis (y-axis) represents Stress ($\sigma$).

2. Curve Sketch:

   • Start from the origin (0,0).
   • Initial Linear Region:
     • Draw a straight line from the origin, increasing linearly. This represents elastic behavior until the proportional limit.
   • Yield Point:
     • At a certain point on the y-axis, mark the yield point where the line begins to curve downward.
   • Strain Hardening Region:
     • The curve should then rise again, indicating the material is entering the strain hardening region.
   • Ultimate Strength:
     • Mark the ultimate strength point, where the curve reaches its maximum before it starts to descend.
   • Necking Region:
     • After the ultimate strength, the curve will start to decline sharply indicating necking and eventual failure.

3. Key Points:

   • Label the yield point (typically denoted as $\sigma_y$), ultimate strength ($\sigma_u$), and fracture point (where the curve meets the x-axis).
   • Show elongation along the x-axis, noting that the curve suggests the material can undergo significant deformation before failure.

Summary:

This sketch should illustrate that cold worked deformed bars have significant elastic and plastic behavior, with noticeable yield and ultimate stress points.

If you require a more technical depiction, please use software tools that can create graphs and charts following mathematical representations.