I was planning to buy an Andel Standard Track crankset. It uses 110mm axle bottom bracket, but the stock bracket on my bike is 103mm. Will this mess up my chainline?
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Not only will it mess with your chainline (as already answered, 3.5mm off inwards), it may happen that you won't be able to mount this crankset at all in the first place.
103mm107mm bottom bracket is standardtypical for road bikes with double or triple chainring in front although 103mm spindles are also available. In practice it means that the largest chainring is set out even more than a single one on a 110mm BB. And often it is just off the chainstay (the distance is only couple of millimetres). To be 100% sure you'd need to check what is the offset of your current crank and the one you want to buy.
Mounting a large chainring on a spindle that is too narrow may (and often does) cause the teeth to grind on the chainstay making pedalling impossible and irreversibly damaging your frame.
Chainline is the least problem here, thus.