$\because \angle B=40^{\circ}$，$\angle C=36^{\circ}$，

$\therefore \angle BAC=180^{\circ}-\angle B-\angle C=104^{\circ}$

$\because AB=BD$

$\therefore \angle BAD=\angle ADB=\left(180^{\circ}-\angle B\right)\div 2=70^{\circ}$，

$\therefore \angle DAC=\angle BAC-\angle BAD=34^{\circ}$

故答案为：$34$.

$\because \angle B=40^{\circ}$，$\angle C=36^{\circ}$，

$\therefore \angle BAC=180^{\circ}-\angle B-\angle C=104^{\circ}$

$\because AB=BD$

$\therefore \angle BAD=\angle ADB=\left(180^{\circ}-\angle B\right)\div 2=70^{\circ}$，

$\therefore \angle DAC=\angle BAC-\angle BAD=34^{\circ}$

故答案为：$34$.