I have had trouble with the trio of traditional characters which simplify to 干. It turns out (as usual) that all three have curious and twisted etymologies. Here are some mnemonics for keeping the traditional characters 幹干and 乾 straight in your head:
This is the most straight-forward of the trio.
It means "dry":
In its qian2 pronunciation, it is also one of the Eight Trigrams, and a surname, but those are much lower frequency uses.
Mnemonic: When there is a drought you beg for even a little mist.
Wieger clarifies that "dry" was originally written using 旱 on the left (with 十 above it?). The character 乾 originally was read qian2 and represented the sun shining into the jungle, dislodging vapors which then rise up into the sky.
This character can mean "to do" or "tree trunk".
It can be used alone:
You have committed ("done") a folly.
Or in the common idiom gan4ma5:
What are you doing?
A canonical example of the "tree trunk" meaning is:
A tree (which originally was made of wood but is now a post-modern clothes hanger pole) is topped with an umbrella of leaves. But, through the mist, you can only see the trunk.
Wieger says the 干 component in 幹 is supposed to be 木, the former being an "absurd phonetic redundancy" This would make more sense.
This is the odd-ball in the group. It has several meanings. Its most prolific meaning is "to offend":
to offend or to violate
But this gan can also mean "stem" in:
the Ten Heavenly Stems
An archaic meaning is "shield":
weapons of war, literally "shield and spear"
In Toronto, up until a couple of years ago, it was illegal to hang clothes outside, i.e. one of the biggest offenses and ways to offend the sensibilities of people was to hang your clothes outdoors. Silly, but unfortunately true. (credit: koohii user vorpal)
Wieger tells us that 干 represents a pestle. By extension it means to grind or destroy. Destruction in the moral sense gives offense. Destruction in the martial sense gives the warlike association in 干戈.