Final answer:
The statement is true; for uniform stress distribution in an axially loaded member, the resultant force must act through the centroid of the cross-sectional area.
Step-by-step explanation:
The statement that 'if the distribution of stress in an axially loaded member is to be uniform, the resultant force must act through the centroid of the cross-sectional area' is true. When a force is applied to a member such as a rod or beam, stress is distributed across its cross-sectional area. Tensile and compressive forces should act perpendicularly to the cross-section and along the member's length to maintain uniform stress. This requires that the resultant force is aligned with the centroid of the cross-section. If the force does not pass through the centroid, it causes bending or torsion, leading to a non-uniform distribution of stress.