Depending on your policy, you may be covered for hidden structural damage. If your policy is the type known as an "all risk" policy, you are probably covered, unless there are specific exclusions related to the damage. There are other factors that need to be considered before filing the claim, though, such as the initial cause of the structural damage and the cost of the repairs versus your deductible.
If the damage was caused by an identifiable and correctable source, your claim may be rejected. For instance, if the home suffers structural damage because of known or visible leak around windows or the ventilation pipes, the insurance can deny the claim on the grounds that you were negligent in the maintenance of the property, violating your obligations under the policy. To complicate this serious even more, your insurance can be made non-renewable if such a finding is made, and that will not only leave you with the out of pocket expenses of the repairs, but in search of a new insurance company as well.
Before you file a claim, calculate the numbers to determine if doing so is in your best interest. If the cost of repairs is only a little more than your policy deductible, it is probably better to make the repairs yourself than to file a claim against your insurance. Keep in mind that the more claims you file, the greater your risk assessment, so renewing the policy may cost more, and if you have a string of claims filed against insurance companies (including auto and health insurance) you find it very expensive to get insurance policies, if you can find a company to accept you at all.