  We investigate the steerability of two-qubit Bell-diagonal states under
projective measurements by the steering party. In the simplest nontrivial
scenario of two projective measurements, we solve this problem completely by
virtue of the connection between the steering problem and the joint-measurement
problem. A necessary and sufficient criterion is derived together with a simple
geometrical interpretation. Our study shows that a Bell-diagonal state is
steerable by two projective measurements iff it violates the
Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict
hierarchy expected between steering and Bell nonlocality. We also introduce a
steering measure and clarify its connections with concurrence and the volume of
the steering ellipsoid. In particular, we determine the maximal concurrence and
ellipsoid volume of Bell-diagonal states that are not steerable by two
projective measurements. Finally, we explore the steerability of Bell-diagonal
states under three projective measurements. A simple sufficient criterion is
derived, which can detect the steerability of many states that are not
steerable by two projective measurements. Our study offers valuable insight on
steering of Bell-diagonal states as well as the connections between
entanglement, steering, and Bell nonlocality.
