Bentley's *Bentley Webinar: Advanced Slab Design in STAAD with FEM models* begins at __25 Jun 2024__

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

Contents [show]

Calculate the shear force and bending moment values due to the imposed loading on the overhanging beam of Figure 1.

The free-body-diagram is shown in Figure 2. The beam’s reactions are calculated as:

ΣF_{x}^{ }= 0 -> **A _{x} = 0**

ΣΜ_{Α} = 0 -> Β_{Y}x6 - 30x10 -5x4x4 = 0-> **Β**_{Y }**=63.33kN **

ΣF_{Y }= 0 -> A_{Υ} + B_{Υ} = 5x4 + 30 -> **A _{y} =-13.33kN**

**Calculations of shear force**

Shear force is calculated in both sides (left and right) of each point.

F_{A-right} = -13.33kN

F_{C} = -13.33kN

F_{B-left} = -13.33 – 5x4 = - 33.33kN

F_{B-right} = -13.33 – 5x4 + 63.33 = +30kN

F_{D-left} = +30kN

**Calculations of bending moment **

Bending moment is calculated as follow (same left and right):

M = 0

M = –13.33x2 = -26.66kNm

M = –13.33x6 – 5x4x2 = –80 –40 = –120kNm

M = 0

**Shear force and bending moment plots**

The following Figure 3 presents the plots of shear force and bending moment.

Some interesting points should be outlined:

1. The maximum bending moment will occur at the point where shear force changes sign. Point B is such a point.

2. The bending moment sign does not change, hence there is no point of contra-flexure. The bending moment diagram is a straight line from point A to C, a parabolic curve from C to B and a straight line from B to D.

Structural AnalysisTruss deflection using the unit load methodMethod of sectionsBending stress in a beam elementCalculation of the cross-sectional area and the position of centroidCalculation of the second moments of area

Buckling

1 pages

Confinement (structural)

Elasticity and Inelasticity

Fatigue

Moment distribution

Nonlinear analysis

Structural stability

1 pages

Determine the shear force and moment acting at a section passing through point C on the beam....

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

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

Given: A simply supported beam of length L=5m is given in Figure 1a. The beam is subjected to...

Draw the shear and moment diagrams for the cantilever beam (units KN,m). Solution...

Given: A pin-jointed truss is given in Figure 1. Determine the vertical displacement of join...

Find the axial forces of the members 2-3, 9-3 of the truss for the given loads. Solution...

Calculate the vertical deflection of the beam (magnitude and direction) at the midpoint of the ce...

Jun, 18, 2019 | Education #### Calculate the Maximum Shear Stress

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

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

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

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

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

Jun, 29, 2023 | Education #### Nominal flexural strength of a reinforced concrete beam

Aug, 21, 2017 | Education #### Calculation Example – Calculate the moments of inertia Ix and Iy.