ARCHES AND CABLESArches

Cables (with concentrated loadings)

Parabolic Cables

Catenary Cables

ARCHES

Receives its load mainly in compression

May resist bending and shear depending on its

loading due to its rigidity

TYPES OF ARCHES

PROBLEM

Determine the reaction components for the three-

hinged arch shown. Support B is 5m below

support A.

CABLES

Support loads over long spans for structures

such as suspension bridges, cable car systems

ad similar structures

Internal forces always acts under tension

ASSUMPTIONS

Cable is perfectly flexible. Resistance to

bending is very small and negligible

Cable is inextensible. Change in length is

negligible and the original length is somewhat

restored after the application of load.

Weight of cable is negligible compared to

the load it supports.

CABLES SUBJECTED TO CONCENTRATED LOADS

Methods of analysis:

1. Method of Joints and Sections

2. General Cable Theorem

“At any point in the cable acted upon by vertical loads,

the product of the horizontal component of the

cable tension and the vertical distance from the

point to the cable is equal to the bending moment

that would occur at that section if the loads carried by

the cable were acting on an end-supported beam of the

same span.”

H x sag = M

PROBLEM

Determine the tension in each segment of the

cable shown. What is the dimension of h?

PARABOLIC CABLES

Cables subjected to uniform loading along the

horizontal.

EQUATIONS (SYMMETRIC)

PROBLEM

A cable carrying 200 N/m along the horizontal is suspended

at two points A and B, A being 20 m lower than B. The two

points are 200 m apart horizontally. If the lowest point C of

the cable is 8m below the level of A, determine the tensions A,

B and C, the sag at the vertex with imaginary chord AB and

the total length of the cable.

Ans. TA = 62246.85 N, TB = 66030.34 N,

TC = 60667.41 N, h = 14.967 m,

STOTAL = 204.51 m

PROBLEM

The cable of a suspension bridge is tied from two supports of

equal elevation at a Z distance apart. Based from design load

criteria, the cable will carry a dead load of 2000 lb/ft and a

live load of 1600 lb/ft. The elevation of the supports and the

lowest point on the cable differs by 9ft. What must be the

value of Z in order to withstand a maximum tension of

100000 lb?

Ans. Z = 38.136 ft.

PROBLEM

The suspension bridge in the figure is constructed using twostiffening trusses that are pin connected at their ends C andsupported by a pin at A and a rocker at B. Determine themaximum tension in the cable IH. The cable has a parabolicshape and the bridge is subjected to a single load of 50 kN.

Ans. TMAX = 46.9 kN

CATENARY CABLE

Loaded uniformly along its length

Example: cable subjected only to its weight

Derivation of equations

for catenary cable

EQUATIONS

PROBLEM

A wire weighing 7.5 kN/m is suspended between

two supports at the same level and 45 m apart. If

the sag of the cable is 15m, what is the maximum

tension in the cable. What is the total length of the

cable?

Ans. TMAX = 254.64 kN, STOTAL = 56.34 m

PROBLEM

A guy wire is hung from two posts of the same

elevation 110 m apart. Compute the total length of

the cable, the sag at the lowest point and the

maximum tension if the cable can support a

minimum tension of 900 N. The wire weighs ¾

kg/m.

Ans. STOTAL = 113.74 m, sag = 12.57 m,

TMAX = 992.52 N

PROBLEM

A uniform flexible cable 200m long weighs 5000 N.

The resultant tensions at the ends of the cable are

8000 N and 8800 N, respectively. What is the

difference in elevation of the two ends? How far is

the lowest point of the cable below the lower end?

What is the horizontal distance between ends?

Ans. ΔZ = 32 m, d = 3.36 m, L = 194.36 m

PROBLEM

A uniform flexible cable weighing 50 N/m has a

span of 180m and a sag of 30 m. Find the

maximum tension and the length of the cable.

Ans. TMAX = 8486.60 N, STOTAL = 192.71 m