Create a free account and view content that fits your specific interests in structural engineering __Learn More__

Contents [show]

**Given: **

A simply supported beam of length L=5m is given in Figure 1a. The beam is subjected to uniform distributed load equal to 3.2kN/m. If the beam has a rectangular cross-section, as shown in Figure 1b, calculate the absolute maximum bending stress in the beam and draw the bending stress diagram.

**Solution:**

The bending stress of a beam element is calculated using the bending equation, i.e. *M / I = σ / y*, where *M *is the bending moment,* I* is the moment of inertia about the neutral axis (N.A.) of the section, *σ* is the bending stress and *y* is the distance from the neutral axis to the point of bending stress. In other words, we can write that:

**σ = M y / I (1)**

The above relation shows that the bending stress will be maximized if the distance *y* becomes maximum, i.e. at the top or bottom of the section. The latter is translated to a distance of 5cm from the neutral axis of the section. It is pointed out that the absolute maximum bending stress concerns the section of the maximum bending moment.

Moreover, the given beam is simply supported with uniform loading on the entire span. Thus, the maximum bending moment will occur at the mid-span of the beam and is calculated following the formula M_{max} = q L^{2}/8, where *q* is the uniform load on the beam and *L* is the span of the beam. The maximum bending moment is:

**M _{max} = 3.2 x 5^{2} / 8 = 10kNm (2)**

For a rectangular section, the moment of inertia I_{xx}, about the neutral axis, is calculated as:

**I _{xx} = bd^{3}/12 = 6 x 12^{3} / 12 = 0.864 x 10^{3}cm^{4} = 0.864 x 10^{-5} m^{4} (3)**

Using Eq. 1, the absolute maximum bending stress is calculated as:

**σ _{max} = (M_{max}) (y_{max}) / (I_{xx}) = 10kNm x 0.06m / (0.864 x 10^{-5}m^{4}) = 0.694 x 10^{5} kN/m^{2} = 69.4 MPa**

The bending stress diagram is shown in Figure 2. The bending stress above the neutral axis (N.A.) is compressive (negative) while the bending stress below the neutral axis is tensile (positive).

A steel bar with diameter d = 14 mm is subjected to a tensile load P = 10 kN (see figure). (a) What...

Calculate the member diagrams for Axial Force N, Shear Force S and bending Moment M for the followin...

Calculate the member diagrams for Axial Force N, Shear Force Q and bending Moment M for the followin...

Calculate the max stress because of torsional moment on the outer layer of a steel hollow rod when t...

Calculate the reactions and member forces. Solution We calculate the reactions. ...

Beam, in structural engineering, is a horizontal structural element that is designed to carry and...

A copper bar with a rectangular cross section is held without stress between rigid supports. The tem...

Sep, 16, 2022 | Education #### Diaphragms

Aug, 05, 2019 | Education #### How to calculate yield strength

Aug, 28, 2023 | Education #### Truss deflection using the unit load method

Mar, 08, 2016 | Education #### Calculation Example – Beam with inner hinge (Part A). Find the Reactions

Sep, 08, 2015 | Education #### Calculation Example: Axial Force On A Column

Oct, 04, 2017 | Education #### Calculation Example – Plastic Neutral Axis.

Jan, 20, 2016 | Education #### Calculation Example - Calculate the Axial Forces on the Truss Members

Sep, 16, 2022 | Education #### Structural stability

Feb, 27, 2024 | Education #### Time History Analysis: process and advantages