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From what I know, a shift in LRAS is generally caused by a change in maximum productive capacity of an economy, which affects the full-employment output level. Such change in maximum productive capacity would also cause a shift in SRAS.
So does this mean whenever LRAS curve shifts SRAS curve will also shift? If not, are there any examples against this?
The SRAS also shifts.
SRAS is normally used in models where the supply side does not adjust immediately to the new conditions in the market, i.e. models with nominal rigidities. Examples are: sticky wages, sticky prices.
Other instances where adjustments in prices or nominal money supply are not immediate and in which money has a real effect are the Lucas 'misperceptions' or 'islands' model or Cash in advance models.
However, and to the point of answering your question, all these models coincide that in the long term and when the agents in the economy have had the time to adjust their choice variables and/or information symmetry is restored, the AS is vertical again (LRAS). So, if there has been sufficient time for the long run AS to adjust, by definition of short run, i.e. shorter than the long run, there has been enough time for the SRAS to adjust as well.
Short answer: Yes, the SRAS curve will shift after the LRAS shifts to return the short-run equilibrium (SRAS/AD) back in line with the long-run equilibrium (LRAS/AD). The reason the SRAS curve doesn't shift immediately with LRAS is that there are so-called "frictions" or "nominal rigidities" such as contracts and information gaps that prevent firms from adjusting supply plans instantly.
Long answer: There are two simple "stories" we can tell to explain the dynamics of the elementary AS/AD model: the "inflation gap" story and the "output gap" story. Both of these stories are compatible with each other, so they're usually taught as both occurring at the same time.
Inflation gap story: SRAS is modeled as shifting upward when expected price levels increase. We can consider the long-run (expected) equilibrium to occur at the intersection of LRAS and AD, and the short-run (actual) equilibrium to occur at the intersection of SRAS and AD. If you start in a long-run equilibrium where all three curves intersect, but then impose an LRAS shock on the model and shift the curve, then the expected price level and actual short-run price level will differ. This is what we call an inflation gap. As firm owners come to the realization that the supply shock is here to stay, they adjust their production processes to match and the SRAS curve shifts to bring the short-run equilibrium in line with the long-run equilibrium.
Output gap story: SRAS is also modeled as shifting whenever prices of factors of production change. Thus the output gap generated by the supply shock becomes relevant, with actual short-run output out of line with the long-run sustainable level marked by the LRAS curve. For example, after a positive LRAS shock, the short-run equilibrium will have less output than the long-run sustainable level. The result is an abundance of resources, and the prices of factors of production will fall, causing firms to increase production and shift the SRAS to the right until actual output matches the long-run sustainable level. An opposite story can be told to explain why SRAS shifts left after a negative LRAS shock.
