**Homework 1**

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We are going to design the highlighted 2 ft strip (pier) between the garage door opening and the window for out-of-plane loads. Pertinent properties are:

Roof dead load: 540 lb/ft

Roof wind uplift: 340 lb/ft

Roof load eccentricity: 5.31 inches towards inside of wall

Wind pressure: 30 psf

Wind suction: 26 psf

Use f’_{m} = 2000 psi, Grade 60 steel, bars in center of wall, 8 inch CMU, and Type S PCL mortar. Assume that the pier is fully grouted (weight of 75 psf), and the rest of the wall has a weight of 42 psf. Neglect the weight of the door and window.

Part | Description | Answer |

A. | Determine the out-of-plane wind load on the pier in terms of kip/ft for the load combination 0.9D+1.0W, wind suction. | |

B. | For the load combination 0.9D+1.0W, determine P_{uf}, the factored load at the roof level. (kips) | |

C. | Determine the location of the maximum moment down from the top of the wall for the load combination 0.9D+1.0W, and wind suction. (ft) | |

D. | Determine the maximum first order moment for the load combination 0.9D+1.0W, and wind suction. (k-ft) | |

E. | Determine the axial force at the location of the maximum moment for the load combination 0.9D+1.0W, and wind suction. (kip) | |

F. | Estimate the required area of steel for the load combination 0.9D+1.0W, and wind suction. (in^{2}) | |

G. | If one bar is used in each of the three cells of the pier, determine the required size of the bar. | |

H. | Determine the cracked moment of inertia for the load combination 0.9D+1.0W, and wind suction. Use the reinforcement from part G. (in^{4}) | |

I. | Calculate the moment magnification factor, ψ, for the load combination 0.9D+1.0W, and wind suction. | |

J. | Calculate the magnified moment, M_{u}for the load combination 0.9D+1.0W, and wind suction. (kip-ft) | |

K. | Determine the ratio of the magnified moment to the design moment for the load combination 0.9D+1.0W, and wind suction. | |

L. | Before checking deflections, we will check the load combination 0.9D+1.0W, but with wind pressure on the wall. Determine the maximum first order moment for the load combination 0.9D+1.0W, and wind pressure. (k-ft) | |

M. | Determine the axial force at the location of the maximum moment for the load combination 0.9D+1.0W, and wind pressure. (kip) | |

N. | Calculate the magnified moment, M_{u}for the load combination 0.9D+1.0W, and wind pressure. (kip-ft) | |

O. | Determine the ratio of the magnified moment to the design moment for the load combination 0.9D+1.0W, and wind pressure. | |

P. | We will check deflections for the load combination D+0.6W, with wind pressure. Determine P_{f}, the load at the roof level. (kips) | |

Q. | Determine the location of the maximum moment down from the top of the wall for the load combination D+0.6W, and wind pressure. (ft) | |

R. | Determine the maximum first order moment for the load combination D+0.6W, and wind pressure. (k-ft) | |

S. | Determine the axial force at the location of the maximum moment for the load combination D+0.6W, and wind pressure. (kip) | |

T. | Determine the cracking moment of the pier. Use the axial load from 0.9D+1.0W, wind suction, for determining the cracking moment. (k-ft) | |

U. | Determine the cracked moment of inertia for the load combination D+0.6W, and wind pressure. Use the reinforcement from part G. (in^{4}) | |

V. | Determine the effective moment of inertia for the load combination D+0.6W, and wind pressure. (in^{4}) | |

W. | Determine the first-order deflection for the load combination D+0.6W, and wind pressure. (inch) | |

X. | Determine the deflection magnification factor for the load combination D+0.6W, and wind pressure. | |

Y. | Determine the magnified deflection for the load combination D+0.6W, and wind pressure. (inch) | |

Z. | Determine the allowable deflection. (inch) | |

AA. | Determine the ratio of the magnified deflection to the allowable deflection for the load combination D+0.6W, and wind pressure. |