**Possible Shear failure on bridge during the Chi-Chi Earthquake (Ref)**

While bending failure is usually found with long beam spans carrying uniform loads, shear is an abrupt force of actually tearing a beam in half. Think of a sheet of cardboard; bending failure would occur after you fold the cardboard in half, and fold it back again, and continue until the cardboard has yielded so much that it no longer has any strength left and is relatively easy to break (we’ve all done this as kids with sticks or anything else we found breakable). Shear would be the force of just tearing the card board in half.

The bending force takes a long time to break something and therefore is allowed a relative low safety factor (the idea is also that you should see bending failure occurring due to high deflections in the system). The shear force is immediate and abrupt, and similar to wire cables, or plastics has a high safety factor.

**Note:** It is important to know that shear force will normally not govern in the design over bending force, unless the member in question is very short in length with very high loads, concrete beams, wood, or a thin walled tube. This is do to the fact that the bending stress will normally increase exponentially with the length of a beam while shear stress will only increase linearly.

How to Understand Shear Force
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## How to Calculate Shear Force (V):

Shear force (aka V) is usually calculated using the Shear and Moment Diagrams.

Force ↔ through differentiation and integration of each other. |

## Examples

### Example #1:

You have an A36 W6*20 spanning 4’ with a distributed load of 2000 plf. What is the shear design ratio?

**Use the following steps:**

1) **Find V** = wl/2 = 4000 plf * 4’ / 2 = 8000 lbs

2) **Find A _{web}** = t’_w_’ * d = 0.258 in * 6.2 in = 1.55 in

^{2}

3)

**Find f**= \frac{V}{A_{web}} = \frac{8000 lbs}{1.55 in^2} = 5161 psi

_{v}4)

**Find F**= 0.4 * F

_{v}_{y}= 0.4 * 36 ksi = 14.4 ksi > f

_{y}= 5.2 ksi

5)

**Shear Design Ratio =**\frac{f_v}{F_v} = \frac{5.2 ksi}{14.4 ksi} = 0.36

### Example #2

Will the Shear Design Ratio or the Bending Design Ratio govern for the following scenario?