Dynamics of Structures
Structural Engineering Simplified
1.3 Springs in Parallel and in Series
Springs in Parallel
When springs are in parallel, the applied forces required to move the mass must stretch both springs with the same amount, hence,
Figure 1.3.1 Springs in Parallel
Springs in Series
When springs are in series, the applied forces required to move the mass stretchs both springs with different amounts, the total stretch is equal to the stretch in all springs,
Figure 1.3.2 Springs in Series
FIgure 1.3.3. Example 1.3.1
Example 1.3.1
A W12x50 steel beam (E = 29000 ksi) is supporting a weight of 250 kips as illustrated in the figure below. Neglecting the weight of the beam itself, determine the total stiffness of the system.
For W12x50, E = 29000 ksi and Ix = 394 in4.
If the mass tries to move vertically, it has to overcome both the stiffness of the beam k1 and the stiffness of the spring k2, the beam will deflect with a value different from the spring deflection, this indicates that the two springs are attached in series,
Notice that the total stiffness is smaller that each of the individual stiffnesses! We will use this calculated stiffness in a future example.