1. All cables carry approximately equal forces due to uniform spacing
2. The cables nearest to the tower carry higher forces due to steeper angles
3. The outermost cables carry the highest forces regardless of angle
4. Cable forces are independent of their arrangement pattern

Explanation

Explaination: In a semi-fan arrangement, cables near the tower are more steeply inclined and carry higher forces due to:

1. Their shorter length and steeper angle results in higher axial forces to support the same vertical load
2. They support additional load from the concentration of cables at the tower top
3. The vertical component of the cable force must be larger to provide the same deck support due to the steeper angle

1. 1,157 kN
2. 2,313 kN
3. 3,270 kN
4. 4,626 kN

Explanation

Explanation: In this cable-stayed bridge system, the total deck load is distributed equally between the two cable planes that support the structure. This load-sharing mechanism means that each individual cable is responsible for carrying exactly half of the total tributary load calculated for that section. The final axial force in each cable is then determined by considering the geometric effect of the cable angle, which transforms the vertical load into an axial force along the cable's length. Among the provided options, choices A and C show common misconceptions in calculating cable forces, specifically in how they handle the angle transformation and load sharing between planes. Option D represents what the force would be if the bridge had only a single cable plane, effectively doubling the force in each cable. See calculation steps below:

1. Total factored load per meter = (1.25 × 120) + (1.7 × 40) = 218 kN/m
2. Total tributary load = 218 kN/m × 15m = 3,270 kN
3. Load per cable plane = 3,270 ÷ 2 = 1,635 kN (since there are two cable planes)
4. Axial force in each cable = 1,635 ÷ sin(45°) = 1,635 ÷ 0.707 = 2,313 kN

Key Learning Points: Understanding cable forces in stayed bridges requires careful consideration of several key factors that influence the final design. Cable forces consistently increase with larger tributary areas, as more deck length must be supported by each cable. Similarly, shallower cable angles result in higher axial forces due to the geometric transformation of loads. Higher deck loads, whether from dead load or live load factors, directly increase the cable forces needed for support. This solution clearly demonstrates how load factors and bridge geometry work together to determine cable requirements. It's important to note that in real-world applications, engineers must also account for additional factors such as cable sag effects, temperature variations, and other environmental conditions that influence the final design forces.