A Model for the Dynamic Analysis of Sheathing-to-Stud Connections

1. A Model for the Dynamic Analysis of Sheathing-to-Stud Connections Harry W. Shenton III & Timothy E. Elliott Department of Civil and Environmental Engineering University of Delaware

2. Background on Modeling Wood Frame Connections • Early static models based on a beam on an elastic foundation (Kuenzi, 1955). • Empirical models extend the analyses into the nonlinear regime. • Most recently, nonlinear FEM analyses for static and dynamic loads.

3. Objectives • Develop an analytical model of a nailed wood connection for studying cyclic/dynamic behavior - that can be used to predict the overall effectivestiffness and energy dissipation of the connection based on the basic geometric and material properties of the connection components. • Verify the accuracy of the model using the results of cyclic tests.

4. Schematic of a Full Connection Framing Sheathing Fastener

5. D (t) = D sin w t o a x k, c Fixed/Rigid Sheathing D (t) Fastener EI w(x,t) Beam on a Viscoelastic Foundation Model

6. Model Formulation

7. Solution for w(x,t)

8. w(x,t) and P(a,t)

9. KE and ED D (t) P P D

10. Experimental Testing

11. Test results used to determine wood VE foundation properties Test Matrix

12. Sample Test Results

13. Calculation of KE and ED KE ED

14. First Cycle Effective Stiffness

15. First Cycle Energy Dissipation

16. Experimental Results • “One domain” nailed wood connections exhibit viscoelastic behavior. Cyclic testing produced hysteresis loops that can be described by their effective stiffness and energy dissipation capacity. • The COV for the majority of the tests was below 20 percent. This is an acceptable level for testing of wood specimens. • Increasing the nail diameter increases the KE and ED of a connection.

17. Analysis Objectives • Solve for the foundation properties (k, c) of the various wood materials based on a subset of the test results. • Use the analytical model with the foundation properties to predict the KE and ED of other tests. • Compare the theoretical predictions with the experimental results to determine the validity and accuracy of the model.

18. Solving for k and c Measured values *Two equations and two unknowns (k and c)

19. 1st Cycle Foundation Properties

20. Solving for k and c With the known value for k0 and c0 of the sheathing or stud we can now solve for the effective stiffness and energy dissipation for other nail diameters and sheathing thickness' *Forward predict KE and ED

21. 1st Cycle KE Predictions

22. 1st Cycle ED Predictions

23. 15/32 inch BC plywood with an 8d nail 15/32 inch BC plywood with a 10d nail Comparison of Predicted and Measured Loops

24. 19/32 inch CDX plywood with a 6d nail 1 inch #2 SPF stud with a 10d nail Comparison of Predicted and Measured Loops

25. Conclusions • The viscoelastic model accurately predicts the effective stiffness, energy dissipation, and overall hysteretic behavior of “one domain” nailed wood connections. • A method has been developed for measuring the stiffness and damping modulii of the wood material. • Over 75 percent of the predicted effective stiffness and energy dissipation values differed by less than 20 percent from their corresponding experimental results. Theoretical hysteresis loops closely matched those obtained during cyclic testing.