# Performance and Measurement Devices for Membrane Buildings in Civil Engineering: A Review
## 3 Performance  
### Mechanical Performance  
#### 3.1.1 Concentrated Load  
In the laboratory, it is not practical to apply uniform loads on the exterior surfaces of structures such as inflatable beams and arches due to features of their shape. External loads are typically applied to one or multiple portions of the structure to evaluate its performance. Loading methods include hanging heavy objects and the forced displacement of the experimental setup [35, 37]. The most fundamental inflatable membrane structures are inflatable arches and inflatable beams. The deformation of an air beam under external load follows the Timoshenko beam theory rather than the Bernoulli beam theory since the influence of shear stress can hardly be ignored [38, 39, 40]. As illustrated in Figure 5, the distribution of the load has a notable impact on the degree of deformation and the magnitude of the ultimate bearing capacity, and the internal pressure of the structure determines the time when wrinkles emerge. The bearing capacity of an inflatable arch and beam after wrinkling was strengthened by attaching reinforcing straps outside, according to [PERSON] et al. [37], and the form of the straps had a considerable impact on the initial stiffness of members. [PERSON] et al. [4] investigated the structural performance of a full-size inflatable arch frame 10.5 m high, 25 m long, and 20 m wide. The spatial action of the structure was demonstrated to play a role in mitigating the deflection of the inflatable arch under load. Under tension, the inflatable arch structure with horizontal coupling beams had a higher lateral stiffness than under compression. Membrane wrinkling had little effect on structural stiffness. The deformation of the structure when the inflatable arch frame was subjected to vertical or horizontal loading is shown in Figure 6.  
Tensairity is a type of hybrid structure in which the shape considerably affects its performance. The tensairity of the spindle shape demonstrated better stiffness under any load condition when compared to the standard cylindrical shape [34]. When the internal pressure of an air beam is low, the lateral deformation under vertical load is greater than the vertical deformation, resulting in insufficient tensairity component coupling [41]. Increasing the air pressure permits the components in the structure to be in a superior state of interaction and simultaneously enhances the stiffness of the structure [42]. However,  
Figure 4: Other types of membrane structures: 1. Membrane roof, 2. Membrane ceiling, 3. Tensairity, 4. A movable laboratory [5, 7, 34, 36]. as shown in Figure 7, the increased amplitude decreases gradually, a phenomenon that also exists in inflatable arches and inflatable beams. The load-displacement curve of the first cycle of the structure under cyclic load differs from the curves of the second and third cycles due to the flexible member in the structure, whereas the curves of the two and three cycles remain comparable [43]. As the compression member in the structure, almost all the compressive loads on the structure are borne by struts, with the air beam essentially bearing none of it [42]. Under the action of shear load, the tendency and magnitude of the deformation of the upper compressive members and the lower tensile members of the structure are considerably different [43; 44]. As the load increases, the strut shifts from a balanced displacement to a maximum displacement located between the midspan and support, while the maximum displacement of the cable remains in the midspan. The entire strut is M-shaped, with a displacement magnitude more significant than the cable. Tensairity modes are classed as in-phase or out-of-phase depending on their relationship with the internal pressure of the air beam [45]. Figure 5: Air beam load–displacement curve [40]. Figure 6: Undeformed and deformed shape of inflatable arch frame [4]. Figure 7: Effect of different internal pressures on tensairity [42]. [PERSON] et al.