The paper "Behaviour of Structures" is a great example of an assignment on physics. Energy methods assume that the total work in a system is equal to the sum of internal work and external work. Suppose that the rigid body is given small, imaginary (virtual) displacement Δ v, then the total virtual work is done, is equal to the sum of virtual work done by internal forces and virtual work done by external forces, Therefore, (Equation 1) The total work is assumed to be zero, thus it is taken that the sum of internal work and external work is zero.
Defining work as the force applied in the same direction of displacement. (Equation 2) Where Fe is the external force applied to the system, δ is the total deflection of the system due to and in the direction with Fe, ni is the internal force applied to member and Δ i is the deflection of the member due to and in the same direction not with ni, but rather with the original load, If an external load W is gradually applied on the pin frame, it produces a displacement of distance δ , the load moves a distance y.
the internal force P produces an extension δ l in the frame. The external work done must be equal to the internal energy stored in the structure. Then ∑ Wy/2 = ∑ Pδ l/2(Equation 3) To the unloaded structure, a unit virtual\load is applied in the direction of δ , resulting in the force u in any member of the frame. If a real load W is applied to the structure gradually, and equate external work to the internal energy, ∑ Wy/2 + 1 x δ = ∑ Pδ l/2 + ∑ ul/δ l(Equation 4) Subtracting the above equations, 1 x δ = =(Equation 5) Where P is the internal force applied by loads and A, l and E are the areas, length of the frame, and the modulus of elasticity respectively and u is the internal force due to virtual load. For a pin-jointed frame, the virtual\load is applied to the frame expecting a deflection which is positive.
If the force is applied in the opposite direction to the deflection, the deflection will be negative (Williams, 2009). The disadvantage of the work-energy method, of equating the internal strain energy to external work is that normally only the deflection due to a single force can be obtained.
The virtual work method gives the procedure of determining deflections and rotations (slopes) at any point in the truss or other structures subjected to a number of loadings (Williams, 2009). Objectives: 1. To determine the deflection of a loaded pin-jointed structure experimentally and compare it with the theoretical deflection calculated using virtual work analysis. Materials needed Dial gauge Load hanger 5 – 20 weights Pin – join structure like as shown in figure 1 Methodology The experiment begins with calibration of the gauge by setting it at zero.
A very light tap on the front of the screen may help in calibration. After assembling the load hanger-on joint G, the gauge reading was recorded. This was treated as no load. The load equal to 20N was added to the load hanger and the reading recorded. The load of 20N was increased to 100N and the deflection reading for 20, 40, 60, 80, and 100N was recorded. The deflections of joint G were then plotted against the load. Using the linear equation, the deflection of a load of 100N was calculated. The theoretical value of deflection was calculated using the virtual work method.
The cross-section is 20mm2 and E is 205kN/mm2.