البنك في الطابق الثاني، لكنني أستعمل المصعد لأنني متعب.

It has three parts:

• البنك في الطابق الثاني = The bank is on the second floor
• لكنني أستعمل المصعد = but I use the elevator
• لأنني متعب = because I am tired

So the overall pattern is:

• a statement of location
• then a contrasting clause with لكنني = but I
• then a reason clause with لأنني = because I

In Modern Standard Arabic, the present tense of to be is usually not said.

So:

• البنك في الطابق الثاني literally looks like the bank in the second floor
• لأنني متعب literally looks like because I tired

But in natural English, these mean:

• The bank is on the second floor
• because I am tired

If you wanted the past, Arabic would normally use كان:

• كان البنك في الطابق الثاني = The bank was on the second floor

Arabic commonly uses في for location in a building, including floors.

So:

• في الطابق الثاني literally = in the second floor/story
• but the natural English meaning is on the second floor

This is just a difference in how the two languages describe location.

Because in Arabic, adjectives normally come after the noun they describe.

So:

• الطابق = the floor
• الثاني = second

Together:

• الطابق الثاني = the second floor

This is the normal noun + adjective order in Arabic.

Because Arabic adjectives agree with the nouns they describe.

If the noun is definite, the adjective must also be definite.

So:

• الطابق = the floor
• الثاني = the second

That is why you get:

• الطابق الثاني = the second floor

This agreement includes:

• definiteness
• gender
• number
• case

Here both words are masculine, singular, and definite.

The prefix الـ means the.

So:

• البنك = the bank
• المصعد = the elevator

Arabic often uses the definite article when the thing is specific or understood from the situation. In this sentence, it sounds like a particular bank and a particular elevator are being talked about, so الـ is natural.

لكنني means but I...

It is made from:

• لكن = but/however
• plus a first-person ending that gives the sense of I

So:

• لكنني أستعمل المصعد = but I use the elevator

You may also see the shorter spelling لكني in many texts. Both are common.

لأنني means because I...

It is made from:

• لأن = because
• plus the first-person ending

So:

• لأنني متعب = because I am tired

A common shorter spelling is لأني. Both are used.

Here متعب means tired, and it is pronounced mutaʿab.

This is useful because, without short vowels, متعب can look ambiguous to a learner:

• مُتْعَب = tired / exhausted
• مُتْعِب = tiring / exhausting

In this sentence, the meaning is clearly tired, so the intended reading is مُتْعَب.

Also:

• if the speaker is male: متعب
• if the speaker is female: متعبة

The verb أستعمل stays the same for both male and female speakers, because it is first person singular.

No. أستعمل is a correct MSA verb meaning I use, but أستخدم is also very common.

So both of these are fine in MSA:

• أستعمل المصعد
• أستخدم المصعد

They both mean I use the elevator.

In fully vocalized MSA, you could read it as:

البنكُ في الطابقِ الثانيِ، لكنني أستعملُ المصعدَ لأنني مُتْعَبٌ.

A few things to notice:

• البنكُ has -u because it is the subject of the opening nominal sentence
• الطابقِ has -i because it comes after في
• الثانيِ matches الطابقِ
• أستعملُ has -u in the normal indicative form
• المصعدَ has -a because it is the direct object
• مُتْعَبٌ is the predicate, so it is nominative

In normal unvocalized writing, these endings are usually not shown, and in pause they are often not fully pronounced.