## Luz, Francis Arjay P.

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Civil Engineering

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**Situation**

The three-hinged arch shown below is loaded with symmetrically placed concentrated loads as shown in the figure below.

The loads are as follows:

$$P_1 = 90 ~ \text{kN} \qquad P_2 = 240 ~ \text{kN}$$

The dimensions are:

$$H = 8 ~ \text{m} \qquad S = 4 ~ \text{kN}$$

Calculate the following:

**1.** The horizontal reaction at *A*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

**2.** The total reaction at *B*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

**3.** The vertical reaction at *C*.

A. 0 | C. 330 kN |

B. 285 kN | D. 436 kN |

**Problem**

The digits of a three-digit number are in arithmetic progression. If you divide the number by the sum of its digits, the quotient is 26. If the digits are reversed, the resulting number is 198 more than the original number. Find the sum of all the digits.

A. 9 | C. 15 |

B. 12 | D. 18 |

**Situation**

The truss shown in is made from timber Guijo 100 mm × 150 mm. The load on the truss is 20 kN. Neglect friction.

Compression parallel to grain = 11 MPa

Compression perpendicular to grain = 5 MPa

Shear parallel to grain = 1 MPa

1. Determine the minimum value of *x* in mm.

A. 180 | C. 160 |

B. 150 | D. 140 |

2. Determine the minimum value of *y* in mm.

A. 34.9 | C. 13.2 |

B. 26.8 | D. 19.5 |

3. Calculate the axial stress of member *AC* in MPa.

A. 1.26 | C. 1.57 |

B. 1.62 | D. 1.75 |