Axial Force in Structure with No Parallel Force

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Does axial force exist in a member of a structure where no force acts parallel to the member?
 
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a force is applied perpendicular to the member
 
I think an example of what you're referring to would be a simply supported beam (horizontal) with a load applied perpendicular to the neutral axis (vertical). In that case, there is a compressive load on one side of the neutral axis and a tensile load on the opposite side of the neutral axis. So basically there are horizontal forces in the beam that create a moment to resist the load acting perpendicular to the beam.