Cables and Arches

When deriving the relations between the force in a cable and its slope, what two key assumptions are made about the cable's properties?

What form does a cable take when it supports several concentrated loads and has negligible weight?

According to the analysis in Section 5.3, what is the shape of a cable subjected to a uniform horizontally distributed vertical load, w0?

In the analysis of a cable under a uniform distributed load, what does the term FH represent?

In Example 5.2, a cable supports a girder weighing 850 lb/ft over a 100 ft span. The supports A and C are at different elevations, 40 ft and 20 ft respectively, above the lowest point B. What is the calculated horizontal distance, x', from the lowest point B to the support C?

What is a funicular arch?

Which type of arch described in Section 5.4 is statically determinate and not affected by settlement or temperature changes?

In the analysis of the three-hinged arch in Example 5.4, which supports a uniform load of 500 lb/ft over a 100 ft span with a 25 ft rise, what is the vertical support reaction at C (Cy)?

What is the primary function of a tie rod in a tied arch?

For the parabolic three-hinged arch in Example 5.4, what are the calculated values for the internal shear (VD) and moment (MD) at point D, located at x = 25 ft?

In the analysis of the three-hinged tied arch in Example 5.5, what is the calculated tension force in the main tie member FAE?

What is the primary difference between a fixed arch and a two-hinged arch in terms of static indeterminacy?

In Example 5.3, a suspension bridge is analyzed. What is the value of the constant horizontal component of cable tension, FH, determined from the analysis?

Why is it necessary to have a ninth equation, often related to cable geometry, to solve for the unknowns in a cable system with several concentrated loads as described in Section 5.2?

What is the equation for a parabolic cable with its origin at the lowest point, as given by Equation 5-9 in Section 5.3?

In Example 5.1, what is the calculated tension in cable segment BC (T_BC)?

Where does the maximum tension in a cable supporting a uniform horizontally distributed load occur?

What is the purpose of analyzing a three-hinged arch by disassembling it at its hinges, as shown in Fig. 5-9?

In Example 5.6, a three-hinged trussed arch with a 40 ft total span and 15 ft center height is designed to have a funicular (parabolic) shape for a symmetric loading. What is the required height, h1, of the joints B and D, which are 10 ft horizontally from the center?

If a cable supports its own weight and no other loads, what is the specific name for the curve it forms?

In Example 5.2, what is the calculated tension in the cable at its lowest point, B (TB)?

What are the components of the three-hinged arch shown in Figure 5-7?

In the tied arch of Example 5.5, what is the compressive force in member CB (FCB)?

If a girder in a suspension bridge has an internal pin at some intermediate point, what effect does this have on the structural analysis?

In Example 5.1, what is the final calculated vertical dimension h?

Why is the parabolic approximation for a cable's shape under its own weight often acceptable in structural applications?

In the context of the three-hinged arch in Figure 5-9, once the support and hinge reactions are found, how are the internal loadings (normal force, shear, moment) at an arbitrary point D determined?

Based on Example 5.4, how does the maximum bending moment in a parabolic arch under a uniform load compare to that in a simply supported beam with the same span and load?

What type of internal force is primarily resisted by an arch, making it essentially an 'inverted cable'?

What is the consequence of using a roller support instead of a hinge for one of the supports of a two-hinged arch?

In Example 5.3, the maximum tension in the cable, Tmax, is calculated using Equation 5-11. What is this calculated maximum tension?

For the three-hinged trussed arch in Example 5.6, what happens to the top cord and diagonal members when the arch has a funicular shape for the symmetric loading?

What is the relationship between the slope of a cable (dy/dx) and the tension components T and FH at any point?

Referring to Example 5.5, what are the vertical support reactions Ay and Ey for the three-hinged tied arch?

According to Figure 5-8, which type of arch is indeterminate to the first degree?

What is the reason a cable offers no resistance to shear or bending?

In Equation 5-8, FH = w0*L^2 / (2h), what do the variables L and h represent?

In the open-spandrel arch bridge shown in Example 5.4, the load is assumed to be uniformly transmitted to the arch ribs. What is the total resultant load on the entire 100 ft span?

Why must the load in each hanger of a suspension bridge be the same to ensure the cable maintains a parabolic shape?

In Example 5.1, the equilibrium of point B is analyzed. The equation `TBA sin(theta_BA) - 4.82 kN sin(32.3) - 3 kN = 0` is used. What does the 3 kN term represent?

What does the term 'springline' refer to in the context of an arch as shown in Figure 5-7?

In the analysis of the tied arch in Example 5.5, the dashed member GF is intended to carry no force. What type of member is GF?

What is the primary reason for analyzing a three-hinged arch in two separate parts, sectioned at the crown hinge?

In the derivation for a cable under uniform load, what does integrating the equation d(T sin(theta))/dx = w0 yield?

What distinguishes a 'tied arch' from other two-hinged or three-hinged arches?

In the context of the cable system in Example 5.1, how many unknown external reactions and unknown cable tensions are there in total?

For the three-hinged arch in Example 5.4, why is the vertical component of the reaction at hinge B (By) equal to zero?

What is the term for the part of an arch between the crown and the springline, as labeled in Figure 5-7?

In the suspension bridge analysis in Example 5.3, how is the equivalent uniform load w0 determined?

What is the force in the vertical member FGC in the tied arch of Example 5.5?