Ive seen 立ち上がる＆乗ってあがる before,yet I can't tell the difference between them and
立つ｜乗る。

For example 早速立ち上がれ！（Hurry and stand up!)

エレベーターに乗ってあがる (=I take the elevator and go up.).

I haven`t seen any other usage for てあがる。
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2017-06-14T15:51:06.157
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question
compounds
How should てあがる be used？
The suffix ～上｛あ｝がる here implies something rising. Sometimes it is used with
other words that may mean directly to rise or to stand for the sake of
emphasis on the rising motion rather than the act of physically moving to
elevate.

> 立｛た｝つ = to stand up  
>  立｛た｝ち上｛あ｝がる = to rise up

For comparison, think of the use of 上｛のぼ｝る as well:

> 立｛た｝ち上｛のぼ｝る = to rise up in a climbing fashion

Compound verbs such as these add color to phrasing that wouldn't be described
solely by using only one of the parts of the compound. Think of what comes to
mind as you read these sentences:

> 空｛そら｝に立｛た｝ち上｛あ｝がった花火｛はなび｝がきれいにパッとしました。  
> The firework that rose up into the sky made a pretty flash.
>
> 花火｛はなび｝が空｛そら｝に立｛た｝ち上｛のぼ｝って行｛い｝きました。  
> The firework climbed up to the sky.
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2017-06-14T22:00:45.023
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answer
First, let's make a clear distinction between `te-form + 上がる` and `masu-stem +
上がる`. The former is just two verbs combined using the te-form. 乗って上がる is not a
set phrase but just consecutive two actions, エレベーターに乗る and 上がる.

The latter form is called compound verbs. Just as in English you can join a
verb and an adverb to describe a distinct action (e.g,. "carry out", "take
off"), in Japanese you can join two verbs and mean something different. The
Japanese language has tons of compound verbs, and there's even [a dedicated
database site for compound verbs](http://vvlexicon.ninjal.ac.jp/en/). 上がる
after the masu-stem is roughly similar to "`verb` + up" in English. 立つ means
"to stand" whereas 立ち上がる means "to stand up". 燃える is "to burn" and 燃え上がる is
"to flame up". `masu-stem + 上がる` also often means "finish ～ing". Some verb
pairs are unpredictable; for example
[盛り上がる](http://jisho.org/word/%E7%9B%9B%E3%82%8A%E4%B8%8A%E3%81%8C%E3%82%8B)
meaning "to get excited." Use the "Search by V2" function of the lexicon above
to find lots of examples. There is no such word as 乗り上がる in Japanese, but
there is
[乗り上げる](http://jisho.org/word/%E4%B9%97%E3%82%8A%E4%B8%8A%E3%81%92%E3%82%8B).
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answer