Weights on a Beam Suspended by Two Cords

A rod hung by its ends shares its weight equally

A rod of uniform weight and thickness suspended by its two ends divides its weight equally between the cords. When one cord moves toward the fixed one, some weight leaves the fixed cord and joins the moved one, in proportion to how far the cord has travelled along the rod.

How weight shifts when a cord is moved

If you move one cord toward the other, weight departs from it and joins the moved cord. That weight has the same proportion to its remainder as the length of rod left outside the cords has to its remainder.

Diminution of weight as the cords approach

As one cord moves toward the middle, the weight leaving the fixed cord relates to the movement as to the span enclosed between the cords. The reduction of weight and the reduction of the cords' distance stay in equal proportion to their wholes.

The quarter-length cord changes the proportion

A movable cord that passes the quarter-point of the rod's length changes the nature of the proportion of its weights with respect to the opposite cord.

Numerical tables of loads on the rod

Repeated columns of fractional quantities (4, 5; 12 1/2; 8; 6 2/5; 128; 400; 20; 32) evaluate the distribution of weight for particular positions of the cords, testing the stated rules numerically.

Metà destra. Calcoli e asta coi numeri:

Con numeri e calcoli:

Asta uguale alla precedente:

A sinistra della precedente:

Sotto la precedente, calcoli e asta coi numeri:

A destra tre aste coi numeri:

In basso, asta con numeri e calcoli:

Angolo inferiore destro:

Meta' sinistra. Asta coi numeri:

A sinistra, asta sospesa a due corde oblique:

A sinistra e scendendo lungo la piega mediana, asta, numeri e calcoli:

A sinistra, asta sospesa coi numeri:

Asta sospesa:

Verso destra, asta sospesa con pesi, numeri e calcoli:

Asta sospesa a tre corde:

Right half. Calculations and a rod with the numbers:

With numbers and calculations:

A rod equal to the preceding one:

To the left of the preceding one:

Below the preceding, calculations and a rod with the numbers:

On the right, three rods with the numbers:

Below, a rod with numbers and calculations:

Lower right corner:

Left half. A rod with the numbers:

On the left, a rod suspended from two oblique cords:

On the left, descending along the central fold, a rod, numbers and calculations:

On the left, a suspended rod with the numbers:

A suspended rod:

Toward the right, a suspended rod with weights, numbers and calculations:

A rod suspended from three cords: