Step 1: Understand the requirement for web dimensions in plate girders.
The clear dimension of the web refers to the distance between adjacent stiffeners or supports in a plate girder. This dimension is crucial for ensuring the stability of the web under shear forces and preventing buckling. According to IS 800:2007, the Indian Standard Code for Steel Structures, the maximum permissible clear span of the web without intermediate stiffeners is given by: $$ \boxed{180t} $$ This ensures that the web remains stable and does not buckle under applied loads.
Step 2: Evaluate other options.
$ 150t $: Too restrictive; unnecessarily limits design flexibility.
$ 160t $: Below the standard limit; may lead to instability.
$ 170t $: Closer but still below the safe limit.
$ 180t $: Matches IS 800:2007 guidelines; correct value.
Step 3: Select the correct option.
Based on IS 800:2007, the least permissible clear dimension of the web is: $$ \boxed{180t} $$