29. DESIGN II

The connection between the beam and the column can be, Fig. 33.1: 1 q b q b q b q q q c c c q b = q c q b = q c M= sK s(q b- q c) q b = q c Flexible Rigid Semi-Flexible Figure 29.1: Flexible, Rigid, and Semi-Flexible Joints

Flexible that is a hinge which can transfer forces only. In this case we really have cantilever action only. In a flexible connection the column and beam end moments are both equal to zero, M = M = 0. The end rotation are not equal, (cid:18) = (cid:18) .

Rigid: The connection is such that (cid:18) = (cid:18) and moment can be transmitted through the beam col connection. In a rigid connection, the end moments and rotations are equal (unless there is an externally applied moment at the node), M = M = 0, (cid:18) = (cid:18) .

Semi-Rigid: The end moments are equal and not equal to zero, but the rotation are different. (cid:18) = (cid:18) , M = M = 0. Furthermore, the difference in rotation is resisted by the spring M = K ((cid:18) (cid:18) ). spring spring col beam

In beam-column connections, different types of joints affect how forces and moments are transmitted between the beam and the column.

• Flexible Connections: These joints allow for rotation and can be thought of as hinges. They can transfer only forces but not moments, meaning the bending moment at the ends of the beam and column is zero (M = 0). This is suitable for structures that require some flexibility, like temporarily erected buildings.

• Rigid Connections: These joints do not permit relative rotation between the beam and column. They effectively transmit moments, so both rotation and moment values are equal. These connections are typically used in taller buildings where stability against lateral loads is a concern.

• Semi-Rigid Connections: These joints allow for some rotation and can still carry moments. The end moments are not equal to zero but are equal between them. The difference in rotation at the ends is usually resisted by spring elements, which means they have some characteristics of both flexible and rigid connections.

Imagine three different types of hinges for a door. A flexible hinge allows the door to swing freely without holding its position; a rigid hinge keeps the door fixed and straight, ensuring it does not move; while a semi-rigid hinge allows the door to open but has a little resistance, making it feel firm but allowing some movement.

For vertical load across the beam rigid connection will reduce the maximum moment in the beam (at the expense of a negative moment at the ends which will in turn be transferred to...

In a rigid frame structure, when vertical loads act on a beam, the way connections respond can significantly affect the overall moment distribution

• When there are vertical loads applied to beams connected rigidly to columns, the rigid connection helps distribute these loads more evenly across the entire frame.
• This leads to a reduction in the maximum bending moment (which can cause excessive sagging) along the section of the beam. Consequently, there can be negative moments (moments acting in the opposite direction) developed at the connections, which are then transferred to the columns.
• The unique loading conditions lead to a more efficient structure overall, preventing failure at critical points by balancing the forces throughout.

Think of a trampoline with four corners made up of rigid poles. When you jump in the center (apply a vertical load), the tension in the poles (rigid connections) allows the trampoline to distribute the impact across all poles instead of just the center, which helps prevent the poles from bending or breaking. Without this distribution, the poles would experience excessive stress.

Design a two-hinged, solid welded-steel arch rib for a hangar. The moment of inertia of the rib is to vary as necessary. The span, center to center of hinges, is to be 200 ft...

Designing a statically indeterminate arch involves several steps:

• Initial Setup: You define the dimensions (span of 200 ft and rib rise of 35 ft) and loads (weight of the roof and snow). The ribs that support the hangar will need to be strong enough to handle these loads.
• Moment of Inertia: This is crucial as it dictates how much bending the arch can withstand before failing. It will vary along the length of the arch, so calculations must be adapted as this parameter changes.
• Segmented Calculation: The arch is divided into segments to apply concentrated loads and analyze forces systematically. Each segment will be calculated for force distribution based on its position and properties.
• Final Check of Design: After running the necessary calculations for each rib segment and their respective demands, ensure they meet the load requirements. If secondary stresses exist, they also need to be verified to ensure long-term stability.

Designing an arch is like planning the support structure for a huge canvas tent at an outdoor event. You must find out how high the tent should be, how much weight the fabric can handle from rain or snow, and build supporting poles that can withstand those challenges without collapsing under pressure.

Determine the effects of rib shortening and temperature changes in the arch rib of Fig. 29.5. Consider a temperature drop of 100 F...

Temperature changes can affect structural integrity, particularly in metal structures like arches:

• Rib Shortening: As temperature drops, materials typically contract. This means the arch ribs may become shorter, potentially inducing internal stresses. Understanding how much shortening will occur at different temperatures is critical to maintaining stability.
• Stress Calculation: Engineers must calculate the stress changes in materials due to this contraction. This helps ensure that the arch can accommodate these changes without failing.

Think of a balloon that's inflated fully. If you take it outside on a cold day, it might lose some air and appear smaller. Similarly, if your balloon was a structural element, that contraction could cause stress points that need to be accounted for in the design, just like engineers need to prepare for the contraction of steel in cold temperatures.

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