Modal verbs with the meaning "should", "ought to": 应该, 应当, 应 and 该
Modal verbs (情态动词) can be used to express possibility, desire, ability, and necessity. Modal verbs cannot appear without a predicate and can only appear in predicate phrases.
What do they have in common
All these modal verbs 应该 
, 应当 , 应 and 该 are translated as "should", "ought to". They are used to express the need to do an action due to certain circumstances. Usually it is an obligation or a moral duty.
, 应当 , 应 and 该 are translated as "should", "ought to". They are used to express the need to do an action due to certain circumstances. Usually it is an obligation or a moral duty.Examples
申请人通常应拥有优秀学位
Applicants should have a good academic performance
shēnqǐng rén tōngcháng yīng yǒngyǒu yōuxiù xuéwèi
孩子应该听父母
Children should obey their parents
háizi yīnggāi tīng fùmǔ
他已经做了该做的事
He did what needed to be done
háizi yīnggāi tīng fùmǔ
The differences between them
应该 and 应当 can be used with other modal verbs, while 应 and 该 cannot be used with them.
Examples
这部电影应该能够让我们发财
This film should make us rich
zhè bù diànyǐng yīnggāi nénggòu ràng wǒmen fācái
你应当能理解
You should be able to understand it
nǐ yīngdāng néng lǐjiě
应该 and 应当 are used almost interchangeably. However, 应该 can only express the need to do something, while 应当 is advisory in nature.
Examples
他应当更小心点儿
He should be more careful
tā yīngdāng gèng xiǎoxīn diǎnr
该 and 应该 indicate that somebody is making an inference which he/she is sure of based on personal experience.
Sentences with 该 usually end with the modal particle 了 . Sentences with 应该 end with the modal particle 吧 .
. Sentences with 应该 end with the modal particle 吧 . Pay attention
In this meaning, the negative adverbs are placed after the modal verb.
Examples
他们应该最晚十点到达吧
They should arrive no later than ten o'clock
tāmen yīnggāi zuì wǎn shí diǎn dàodá ba
都八点了，她该回来了
It's eight o'clock. She should be back
dōu bā diǎn le, tā gāi huílái le
这应该不奇怪
It shouldn't be surprising
zhè yīnggāi bù qíguài
In exclamatory sentences, 该 gives more emotional coloring. The other verbs don't have this feature.
Examples
我们的责任该有多重啊！
How great is our responsibility!
wǒmen de zérèn gāi yǒu duōchóng a
The verbs also differ in their usage.
应 is used in written language more often than 应该 and 应当.
应该 and 应当 can be used in both written and spoken language.
该 is used in spoken language.