There are multiple limits that apply to some donations in certain situations. For example, If you make non-cash contributions (e.g. appreciated stock) to a 50% limit organization, your deduction for the non-cash contributions is limited to 50% of your AGI minus your cash contributions subject to the 60% limit. So in your example above, if AGI was $100K, then your deduction for appreciated stock would be calculated as $50,000 (50% of AGI) - $30,000 (Cash Contribution) = $20,000 limit on deduction for stock (appreciated assets).
When multiple limits apply there is a series of steps you must follow to determine the amount of your contributions that you can deduct. IRS Publication 526 -Charitable Contributions details the The Limits on Deductions and How To Figure Your Deduction When Limits Apply.
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