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Degrees of Sum of freedom Mean Source Squares Squares Treatments 4 10774.8C x Error 30 Total 34

Degrees of Sum of freedom Mean Source Squares Squares Treatments 4 10774.8C x Error 30 Total 34

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Study of Axial Stiffness in Metal Plate-Connected Trusses A study was conducted on the properties of metal plate-connected trusses used for roof support. The objective was to observe the axial stiffness index (kips/in.) for various plate lengths (4, 6, 8, 10, and 12 inches). #### Observations - **Plate length 4 in:** 311.2, 409.5, 311.0, 326.5, 316.8, 349.8, 309.7 - **Plate length 6 in:** 427.1, 347.2, 361.0, 404.5, 331.0, 348.9, 381.7 - **Plate length 8 in:** 388.4, 366.2, 351.0, 357.1, 409.9, 367.3, 382.0 - **Plate length 10 in:** 343.7, 452.9, 461.4, 433.1, 410.6, 384.2, 362.6 - **Plate length 12 in:** 408.4, 441.8, 419.9, 410.7, 473.4, 441.2, 465.8 ### Hypothesis Testing The study aims to determine if variation in plate length affects the true average axial stiffness using analysis of variance (ANOVA). The relevant hypotheses are: - **\(H_0\):** \(\mu_1 = \mu_2 = \mu_3 = \mu_4 = \mu_5\) - **\(H_a\):** At least two \(\mu_i\)'s are unequal ### ANOVA Table The hypothesis was tested using ANOVA with a significance level (\(\alpha\)) of 0.01. Below is the structure of the ANOVA table used in the analysis: | Source | Degrees of Freedom | Sum of Squares | Mean Squares | \(F\) | |--------------|--------------------|----------------|--------------|-------| | Treatments | 4 | 10774.8 | | | | Error | 30 | | | | | Total | 34 | | | |
Transcribed Image Text:### Study of Axial Stiffness in Metal Plate-Connected Trusses A study was conducted on the properties of metal plate-connected trusses used for roof support. The objective was to observe the axial stiffness index (kips/in.) for various plate lengths (4, 6, 8, 10, and 12 inches). #### Observations - **Plate length 4 in:** 311.2, 409.5, 311.0, 326.5, 316.8, 349.8, 309.7 - **Plate length 6 in:** 427.1, 347.2, 361.0, 404.5, 331.0, 348.9, 381.7 - **Plate length 8 in:** 388.4, 366.2, 351.0, 357.1, 409.9, 367.3, 382.0 - **Plate length 10 in:** 343.7, 452.9, 461.4, 433.1, 410.6, 384.2, 362.6 - **Plate length 12 in:** 408.4, 441.8, 419.9, 410.7, 473.4, 441.2, 465.8 ### Hypothesis Testing The study aims to determine if variation in plate length affects the true average axial stiffness using analysis of variance (ANOVA). The relevant hypotheses are: - **\(H_0\):** \(\mu_1 = \mu_2 = \mu_3 = \mu_4 = \mu_5\) - **\(H_a\):** At least two \(\mu_i\)'s are unequal ### ANOVA Table The hypothesis was tested using ANOVA with a significance level (\(\alpha\)) of 0.01. Below is the structure of the ANOVA table used in the analysis: | Source | Degrees of Freedom | Sum of Squares | Mean Squares | \(F\) | |--------------|--------------------|----------------|--------------|-------| | Treatments | 4 | 10774.8 | | | | Error | 30 | | | | | Total | 34 | | | |
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