Methods for estimating strength and stiffness requirements should be conservative, in that they should overestimate rather than underestimate. The success rate of such a method can be measured by the probability of an overestimate. The article "Discrete Bracing Analysis for Light-Frame Wood-Truss

Question

Methods for estimating strength and stiffness requirements should be conservative, in that they should overestimate rather than underestimate. The success rate of such a method can be measured by the probability of an overestimate. The article "Discrete Bracing Analysis for Light-Frame Wood-Truss Compression Webs" (M. Waltz, T. McLain, et al., Journal of Structural Engineering, 2000:1086-l093) presents the results of an experiment that evaluated a standard method (Plaut's method) for estimating the brace force for a compression web brace. In a sample of 380 short test columns (4 to 6 ft in length), the method overestimated the force for 304 of them, and in a sample of 394 long test columns (8 to 10ft in length), the method overestimated the force for 360 of them. Find a 95% confidence interval for the difference between the success rates for long columns and short columns.

Accepted Answer

The number of successes in the sample of short columns is X = 304, and the number of successes in the sample of long columns is Y = 360. The numbers of trials are [latex]n_X[/latex] = 380 and [latex]n_Y=394[/latex]. We compute [latex] ilde{n}_X=382, ilde{n}_Y=396, ilde{p}_X=(304+1) / 382=0.7984[/latex] and [latex] ilde{p}_Y=(360+1) / 396=0.9116[/latex]. The value of [latex]z_{\alpha/2}[/latex] is 1.96.The 95% confidence interval is [latex]0.9116-0.7984 \pm 1.96 \sqrt{(0.7984)(0.2016) / 382+(0.9116)(0.0884) / 396}[/latex] , or 0.1132 ± 0.0490.

Question 7.4: Methods for estimating strength and stiffness requirements s...

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