Question 7.3: Determine the horizontal and vertical components of the defl...
Determine the horizontal and vertical components of the deflection at joint B of the truss shown in Fig. 7.7(a) by the virtual work method.
Real System The real system and the corresponding member axial forces (F) are shown in Fig. 7.7(b).
Horizontal Deflection at B, Δ_{BH} The virtual system used for determining the horizontal deflection at B consists of a 1-kN load applied in the horizontal direction at joint B, as shown in Fig. 7.7(c). The member axial forces (F_{v1}) due to this virtual load are also shown in this figure. The member axial forces due to the real system (F) and this virtual system (F_{v1}) are then tabulated, and the virtual work expression given by Eq.(1(\Delta) =\sum{F_{v}(\frac{FL}{AE})} (7.23)) is applied to determine Δ_{BH}, as shown in Table 7.3.
| TABLE 7.3 | ||||||
| Member | L (m) |
F (kN) |
F_{v1} (kN) |
F_{v1}(FL) (kN^2-m) |
F_{v2} (kN) |
F_{v2}(FL) (kN^2-m) |
| AB | 4 | 21 | 1 | 84 | 0.43 | 36.12 |
| BC | 3 | 21 | 0 | 0 | 0.43 | 27.09 |
| AD | 5.66 | -79.2 | 0 | 0 | -0.61 | 273.45 |
| BD | 4 | 84 | 0 | 0 | 1 | 336.00 |
| CD | 5 | -35 | 0 | 0 | 0.71 | 124.25 |
| \sum{F_v(FL)} | 84 | 796.91 | ||||
(1 kN)\Delta_{BH} = \frac{84}{200(10^6)(0.0012)}\frac{kN . m}{kN – m}
\Delta_{BH} = 0.00035 m
\Delta_{BH} =0.35 mm\longrightarrow
1(\Delta_{BV}) = \frac{1}{EA}\sum{F_{v2}(FL)}
(1 kN)\Delta_{BV} = \frac{796.91}{200(10^6)(0.0012)}\frac{kN . m}{kN – m}
\Delta_{BV} = 0.00332 m
\Delta_{BV} =3.32 mm\downarrow
Vertical Deflection at B, \Delta_{BV} The virtual system used for determining the vertical deflection at B consists of a 1-kN load applied in the vertical direction at joint B, as shown in Fig. 7.7(d). The member axial forces (F_{v2}) due to this virtual load are also shown in this figure. These member forces are tabulated in the sixth column of Table 7.3, and \Delta_{BV} is computed by applying the virtual work expression (Eq. (1(\Delta) =\sum{F_{v}(\frac{FL}{AE})} (7.23))), as shown in the table.
