# Maximum Flexural Stress

## Support Added at the Midspan of Simple Beam to Prevent Excessive Deflection

**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 |

## Stresses of Hollow Circular Tube Used as a Pole

**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 |

## Strength of Temporary Earth Retaining Wall Made from Wooden Planks

**Situation**

A temporary earth retaining wall consists of wooden plank driven vertically into the ground. The wall is designed to resist 2.4 m height of soil.

Cross-sectional dimensions of the plank = 300 mm wide × 75 mm thick

Allowable bending stress of the plank = 10.4 MPa

Allowable shear stress of the plank = 0.8 MPa

Unit weight of retained soil = 17.3 kN/m

^{3}

Active earth pressure coefficient = 1/3

1. Calculate the maximum flexural stress.

A. 12.7 MPa | C. 8.6 MPa |

B. 14.2 MPa | D. 10.1 MPa |

2. Calculate the maximum shear stress.

A. 1.11 MPa | C. 0.99 MPa |

B. 0.33 MPa | D. 0.77 MPa |

3. Calculate the minimum thickness of the plank to prevent failure.

A. 90 mm | C. 110 mm |

B. 80 mm | D. 100 mm |

## Problem 1003 | Maximum stresses in wood and steel of composite beam

**Problem 1003**

A simply supported beam 4 m long has the cross section shown in Fig. P-1002. It carries a uniformly distributed load of 20 kN/m over the middle half of the span. If n = 15, compute the maximum stresses in the wood and the steel.