Bentley's *Bentley Webinar: Complete workflow of Designing a Concrete Structure* begins at __27 Aug 2024__

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

Contents [show]

**Given:**

A pin-jointed truss is given in Figure 1. Determine the vertical displacement of joint E using the unit load method. All the members have cross-sectional area of 250mm and same modulus of elasticity 200GPa.

**Solution:**

According to the unit load method, which is also known as virtual work method, the deflection of a joint of truss is given by the formula: δ_{Ε} = (ΣNnL)/AE.

The member forces should be calculated two times. First we will calculate member forces "N" due to the real loading and then "n" due to unit virtual load applied at the point of required deflection (in this case joint E). Tensile forces are considered as positive and compressive forces as negative. L is the length of the member, A is area of cross-section of the member and E is modulus of elasticity of the material.

**Step 1**: The member forces "N" due to real load are calculated as follows:

(i) ΣF_{x} = 0 -> C_{x} - 15 = 0 -> **C _{ x} =15kN**

(ii) ΣF_{y} = 0 -> A_{y} + C_{y} - 25 -10 - 20 = 0 -> A_{y} + C_{y} = 55

(iii) ΣM_{z} = 0 ->; A_{y} x 0 + C_{y} x 4 – C_{x} x 0 - 20 x 2 + 15 x 2 - 10 x 2 + 25 x 0 =0 -> **C _{y} = 7.5kN**

Therefore, **A _{y} = 47.5kN**.

It is outlined that it has been considered that z-axis is perpendicular to the plane and passes through joint A.

**Step 2**: Calculation of member forces "n" due to unit virtual load applied at E as shown in Figure 2. As the unit load is applied at center of the truss, the support reactions at A and C will be both 0.5kN. Considering the equilibrium of joint D, we get F_{DE} =0 and F_{DC} =0. Similarly, the equilibrium conditions at joint F gives F_{FE} =0 and F_{FA} =0. Consider the equilibrium of joint B along y-axis we get F_{BE} =0. Considering the equilibrium of joint A gives the following.

(i) ΣF_{y} = 0 -> F_{AE} sin45 + A_{y} - F_{AF} = 0 -> F_{AE} sin45 + 0.5 - 0 =0 -> F_{AE} = -0.5/sin45 = -0.707kN

Structural AnalysisMethod of sectionsBending stress in a beam elementOverhanging beam: shear force and bending moment calculationCalculation 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

Please determine the forces in the members BC, GC and GF of the pin-jointed plane truss shown in F...

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

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

Compute the nominal flexural strength Mn of the reinforced concrete rectangular section of Figure...

Calculate the reactions and member forces. Solution We calculate the reactions. Section 1 0...

Calculate the distance x for locating point load so that the moment on the beam at point B is zero....

Find the maximum moment of the above beam which is subjected to triangular vertical load. SOLUTION:...

The friction coefficient is c1=0.2 between two bodies A,B. The friction coefficient is c2=0.18 betwe...

The stress-strain diagram for a steel rod is shown and can be described by the equation ε=0.20(1e-06...

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

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

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

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

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

Mar, 01, 2024 | Education #### Overhanging beam: shear force and bending moment calculation

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

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