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Based on the improved first order Taylor interval expansion, a new interval analysis methodfirst order Taylor interval expansion, the first order derivative terms of the function are also considered tobe intervals. Combining the improved first order Taylor series expansion and the interval extension offunction, the new interval analysis method is derived. The present method is implemented for acontinuous beam and a frame structure. The numerical results show that the method is more accurate thanthe one based on the conventional first order Taylor expansion.