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This test problem explains and demonstrates the application of temperature gradient to bridge objects. To summarize the process, temperature gradient is specified and applied to the transformed section, axial force (P) and moment (M3) are calculated, then an equivalent temperature distribution (constant + linear) is applied over the depth.
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Example 1: Bridge-modeler model
Please note that the hand calculations attached provide additional details.
A single-span concrete-box bridge, fixed at both abutments, is created using the bridge modeler. The linked bridge object is updated as a solid model. Loading from temperature gradient is defined as shown in Figure 1:
Figure 1 - Temperature-gradient loading
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As mentioned earlier, an equivalent constant + linear temperature gradient generates the temperature load for a solid model. This procedure correlates precisely with the attached hand calculations , as shown in Figure 2:
Figure 2 - Temperature-gradient loading on solid elements
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For bridge response, loading from the temperature gradient induces a moment of 2568 kip-ft, which closely correlates with the hand calculated moment of 2669 kip-ft. Software output is shown in Figure 3:
Figure 3 - Moment induced by temperature gradient
Example 2: Single frame-element model
Please note that the hand calculations attached provide additional details.
For example 2, a single, beam frame element is fixed at both ends and manually loaded with the constant + linear temperature gradient. Element cross section is defined to match those properties of the entire bridge deck section from example 1. The temperature-gradient loading creates a moment of 2668 kip-ft, nearly identical to the hand-calculated moment of 2669 kip-ft. Software output is shown in Figure 4:
Figure 4 - Temperature-gradient on the frame-element model
Attachments
SAP2000 V14.0.0 models (zipped .SDB files) – Example 1: Bridge-modeler model, Example 2: Single frame-element model
Hand calculations (PDF)
Metadata
Name: Temperature-gradient loading for bridge objects
Description: This test problem demonstrates CSI Software calculation and application of temperature-gradient loading to bridge objects.
Program: SAP2000
Program Version: 14.0.0
Model ID: 97