# Structural Engineering and Construction

Engineering Mechanics, Mechanics of Materials, Structural Analysis, Design of Timber Structures, Design of Steel Structures, Reinforced Concrete Structures, Construction and Management

- Read more about Maximum stresses on a pole subjected to combined loadings
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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 |

- Read more about Support reactions of a symmetrically-loaded three-hinged arch structure
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**Situation**

A simply supported beam has a span of 12 m. The beam carries a total uniformly distributed load of 21.5 kN/m.**1.** To prevent excessive deflection, a support is added at midspan. Calculate the resulting moment (kN·m) at the added support.

A. 64.5 | C. 258.0 |

B. 96.8 | D. 86.0 |

**2.** Calculate the resulting maximum positive moment (kN·m) when a support is added at midspan.

A. 96.75 | C. 108.84 |

B. 54.42 | D. 77.40 |

**3.** Calculate the reaction (kN) at the added support.

A. 48.38 | C. 161.2 |

B. 96.75 | D. 80.62 |

- Read more about Simply Supported Beam with Support Added at Midspan to Prevent Excessive Deflection
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**Situation**

A cantilever beam, 3.5 m long, carries a concentrated load, *P*, at mid-length.

**Given:**

*P*= 200 kN

Beam Modulus of Elasticity,

*E*= 200 GPa

Beam Moment of Inertia,

*I*= 60.8 × 10

^{6}mm

^{4}

**1.** How much is the deflection (mm) at mid-length?

A. 1.84 | C. 23.50 |

B. 29.40 | D. 14.70 |

**2.** What force (kN) should be applied at the free end to prevent deflection?

A. 7.8 | C. 62.5 |

B. 41.7 | D. 100.0 |

**3.** To limit the deflection at mid-length to 9.5 mm, how much force (kN) should be applied at the free end?

A. 54.1 | C. 129.3 |

B. 76.8 | D. 64.7 |

- Read more about Limit the Deflection of Cantilever Beam by Applying Force at the Free End
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**Situation**

A simply supported steel beam spans 9 m. It carries a uniformly distributed load of 10 kN/m, beam weight already included.

**Given Beam Properties:**

Area = 8,530 mm

^{2}

Depth = 306 mm

Flange Width = 204 mm

Flange Thickness = 14.6 mm

Moment of Inertia,

*I*= 145 × 10

_{x}^{6}mm

^{4}

Modulus of Elasticity,

*E*= 200 GPa

1. What is the maximum flexural stress (MPa) in the beam?

A. 107 | C. 142 |

B. 54 | D. 71 |

2. To prevent excessive deflection, the beam is propped at midspan using a pipe column. Find the resulting axial stress (MPa) in the column

**Given Column Properties:**

Outside Diameter = 200 mm

Thickness = 10 mm

Height = 4 m

A. 4.7 | C. 18.8 |

B. 9.4 | D. 2.8 |

3. How much is the maximum bending stress (MPa) in the propped beam?

A. 26.7 | C. 15.0 |

B. 17.8 | D. 35.6 |

- Read more about Support Added at the Midspan of Simple Beam to Prevent Excessive Deflection
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**Situation**

A 12-m pole is fixed at its base and is subjected to uniform lateral load of 600 N/m. The pole is made-up of hollow steel tube 273 mm in outside diameter and 9 mm thick.

1. Calculate the maximum shear stress (MPa).

A. 0.96 | C. 1.39 |

B. 1.93 | D. 0.69 |

2. Calculate the maximum tensile stress (MPa).

A. 96.0 | C. 60.9 |

B. 69.0 | D. 90.6 |

3. Calculate the force (kN) required at the free end to restrain the displacement.

A. 2.7 | C. 27 |

B. 7.2 | D. 72 |

- Read more about Stresses of Hollow Circular Tube Used as a Pole
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**Situation**

A concrete beam with cross section in Figure CO4-2B is simply supported over a span of 4 m. The cracking moment of the beam is 75 kN·m.

1. Find the maximum uniform load that the beam can carry without causing the concrete to crack, in kN/m.

A. 35.2 | C. 33.3 |

B. 37.5 | D. 41.8 |

2. Find the modulus of rapture of the concrete used in the beam.

A. 4.12 MPa | C. 3.77 MPa |

B. 3.25 MPa | D. 3.54 MPa |

3. If the hallow portion is replaced with a square section of side 300 mm, what is the cracking moment of the new section in kN·m?

A. 71.51 | C. 78.69 |

B. 76.58 | D. 81.11 |

- Read more about Hollow Circular Beam with Known Cracking Moment
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**Situation**

A beam 100 mm × 150 mm carrying a uniformly distributed load of 300 N/m rests on three supports spaced 3 m apart as shown below. The length *x* is so calculated in order that the reactions at all supports shall be the same.

1. Find *x* in meters.

A. 1.319 | C. 1.217 |

B. 1.139 | D. 1.127 |

2. Find the moment at *B* in N·m.

A. -240 | C. -242 |

B. -207 | D. -226 |

3. Calculate the reactions in Newton.

A. 843.4 | C. 863.8 |

B. 425.4 | D. 827.8 |

- Read more about Continuous Beam With Equal Support Reactions
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**Situation**

A beam of uniform cross section whose flexural rigidity *EI* = 2.8 × 10^{11} N·mm^{2}, is placed on three supports as shown. Support *B* is at small gap Δ so that the moment at *B* is zero.

1. Calculate the reaction at *A*.

A. 4.375 kN | C. 5.437 kN |

B. 8.750 kN | D. 6.626 kN |

2. What is the reaction at *B*?

A. 4.375 kN | C. 5.437 kN |

B. 8.750 kN | D. 6.626 kN |

3. Find the value of Δ.

A. 46 mm | C. 34 mm |

B. 64 mm | D. 56 mm |

- Read more about Continuous Beam With a Gap and a Zero Moment in Interior Support
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**Problem**

A tensile load of 8000 kg elongates a 1-m long square rod by 1 mm. Steel modulus of elasticity is 2 × 10^{6} kg/cm^{2}. What is the dimension of a side of the rod?

A. 5 cm | C. 2 cm |

B. 1 cm | D. 4 cm |

- Read more about Cross-Sectional Dimensions of Steel Rod to Elongate 1-mm when Subjected to 8,000 kg of Tension Force
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