  A grounded 1-bend string graph is an intersection graph of a set of polygonal
lines, each with one bend, such that the lines lie above a common horizontal
line $\ell$ and have exactly one endpoint on $\ell$. We show that the problem
of finding a maximum clique in a grounded 1-bend string graph is APX-hard, even
for strictly $y$-monotone strings. For general 1-bend strings, the problem
remains APX-hard even if we restrict the position of the bends and end-points
to lie on at most three parallel horizontal lines. We give fast algorithms to
compute a maximum clique for different subclasses of grounded segment graphs,
which are formed by restricting the strings to various forms of $L$-shapes.
