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Here's my first attempt at a riddle, hopefully it's not too obvious. Answers should include explanations for each line.

I'm always stepped on by others, but I don't care.
I am strong as wood and cold as stone.
I can never win a race; the closest I come is a tie.
I'm often mistaken for a story.

Who am I?

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Also inspired by CodeNewbie's answer. Are you

a FLOOR?

I'm always stepped on by others, but I don't care.

This line is obvious.

I am strong as wood and cold as stone.

Floors can be made out of wood or stone.

I can never win a race; the closest I come is a tie.

In mathematics, the floor function $\lfloor x \rfloor$ can never exceed $x$; the best it can do is to equal $x$ if $x$ is an integer.

I'm often mistaken for a story.

A building's storeys can also be called its floors.

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  • $\begingroup$ Ding ding ding! $\endgroup$ – erdekhayser Jun 27 '15 at 23:06
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    $\begingroup$ OP has not heard of under-floor heating? $\endgroup$ – Bob Jun 29 '15 at 0:17
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Is it

a step on a staircase?

I'm always stepped on by others, but I don't care.

You step on the steps to go up or down.

I am strong as wood and cold as stone.

A staircase can be made of wood or stone.

I can never win a race; the closest I come is a tie.

Stuck with this one...

I'm often mistaken for a story.

Steps can take you to another 'storey' of the building

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  • $\begingroup$ That's pretty close, but not exactly the answer I was going for. The right answer has many of the same answers but also explains the clue that your answer doesn't. $\endgroup$ – erdekhayser Jun 27 '15 at 18:37
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Inspired by CodeNewbie's answer

I am

an escalator

I'm always stepped on by others, but I don't care.

people are stepping on me, but I don't care since it's my purpose

I am strong as wood and cold as stone.

I am made of steel thus making me strong and cold

I can never win a race; the closest I come is a tie.

I can never be ahead of people since I am always looping. I can be tie when people end their journey on me

I'm often mistaken for a story.

Escalator can take you to another 'storey' of the building

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  • $\begingroup$ Good guess, but that's not it either. $\endgroup$ – erdekhayser Jun 27 '15 at 19:11

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