Opamp-bjt circuit question
It looks like it's intended to sit with output at 0V (or slightly off 0V depending on the bias current and offset voltage of the amplifier), meaning Ic = Vdd/1K since the non-inverting input is at virtual ground (and since R1/R4 are symmetric about ground they (ideally) have no effect). The beta does not enter into the calculation. 

It won't work using the LT1001, for the reason @ThePhoton indicates (the output can't swing down to -Vdd + 0.6V or so) but also the additional gain from the transistor means that this circuit, when made with realistic parts, is actually an oscillator which will not yield a stable DC output value. 



Edit: 

Here is an LTspice simulation that illustrates the above using the op-amp you tried. I have added a -15V supply for the op-amp to deal with the first problem and made the transistor into an integrator via  R6/C1 to deal with the stability issue.