A timber beam AB of span 5 m, width 100 mm and height 200 mm is to support three concentrated loads shown in the figure. The selected grade of timber has following material allowables ; τ_{all}=1 MPa and σ_{all}=10
MPa.

Calculate the maximum shear and normal stresses for the selected timber beam for the given loading conditions.

**Step 1 :** Write down input parameters (including material properties) which are
defined in the sample example.

INPUT PROPERTIES SUMMARY | ||

Parameter | Value | |

Timber width [b] | 200 | mm |

Timber height [H] | 100 | mm |

Allowable shearing stress [τ_{all}] |
1 | MPa |

Allowable normal stress [σ_{all}] |
10 | MPa |

Type of Beam Design |
Simply supported beam
with multiple point loads |

Step 2 : Visit "Simply Supported Beam Deflection Calculation Example" page to see calculation example for shear force and bending moments. Calculate shear forces and bending moments by using Simply Supported Beam Stress and Deflection Calculator as explained in the example. Maximum shear forces and bending moments through the timber beam have been summarized below.

SHEAR FORCES AND BENDING MOMENTS | ||

Distance x | Shear Force (N) | Bending Moment (Nm) |

0.5 | 12676.5 | 6323 |

1.5 | 2500 | 8882 |

Step 3 : Visit "Rectangular Beam Design For Strength" page to calculate maximum shear and normal stresses.

See the sample calculation below for the first point given in the Step 2.

INPUT PARAMETERS | ||

Parameter | Value | |

Structural Beam Height [2c] | 200 | mm |

Structural Beam Width [b] | 100 | |

Height y [y] | 100 | |

Shear Force [V] | 12676.5 | N |

Bending Moment [M] | 6323 | N*m |

OUTPUT PARAMETERS | ||

Parameter | Value | |

Cross section area [A] | 20000 | mm^2 |

First moment of area for the portion of the cross section above point y [Q] |
0 | mm^3 |

Second moment of area [I_{zz}] |
66666668 | mm^4 |

Normal stress at point y [σ_{x}] |
9.484 | MPa |

Shear stress at point y [τ_{xy}] |
0 | |

Von Mises stress at point y [σ_{v}] |
9.484 | |

Maximum normal stress [σ_{max}] |
9.484 | |

Maximum shear stress [τ_{max}] |
0.951 | |

Maximum Von Mises stress [σ_{v_max}] |
9.484 |

Step 4 : Results for stress calculations are summarized in the following table.

RESULTS | ||||

Distance x | Shear Force (N) | Bending Moment (Nm) |
Max. Normal Stress (MPa) |
Max. Shear Stress (MPa) |

0.5 | 12676.5 | 6323 | 9.484 | 0.951 |

1.5 | 2500 | 8882 | 13.323 | 0.188 |

According to results, the design is not safe for the given parameters and conditions. Maximum normal stress (13.323 MPa) is larger than allowable value (10 MPa) given in the problem. A larger size timber beam shall be selected for a safe design.

The problem is fully solved with calculators and examples which are summarized as follows.

Calculator | Usage |

Solid Rectangular Bar - Sectional Properties Calculator | To calculate sectional properties of rectangular solid bar. |

Simply Supported Beam Stress and Deflection Calculator | To calculate forces, moments, stresses, deflections and slopes in a simply supported beam for multiple point loads, distributed loads and concentrated moments. |

Simply Supported Beam Deflection Calculation Example | An example on calculation of max. deflection, max. shear force, max. bending moment and mid-span slope/deflection of a simply supported beam under multiple point loads and a distributed load. |

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