bēng is the core reading, to stretch something taut: 绷紧 (to pull tight), 绷带 (bandage), 绷子 (embroidery hoop). The Internet phrase 绷不住 (can't keep it together, lose composure) also takes bēng. A separate reading běng covers keeping a straight face.
mistakes
Don't confuse 绷 with 崩 (to collapse) or 蹦 (to bounce). All three share the 朋 phonetic but differ by radical and meaning.
Left silk radical, the side form of 糸, twisted strands of silk. 绷 originally meant to bind something tightly with silk cord, hence to stretch taut. Same family: 绑, 绳, 紧, every cord-and-binding verb.
Right 朋 supplies the sound, péng drifting to bēng through a p and b alternation, and the related 蹦 (to bounce) shares the same phonetic. 朋 itself pictures two strings of cowries hung side by side, hence pair and friend. Pure phonetic here; the meaning doesn't carry over.