1) Develop method to find shear stress in a beam. 2) Concept of shear flow and shear stress will be covered. Dr. Ali Al-Gadhib 3) Design of built-up member to resist a given load. Shear in straight member Dr. Ali Al-Gadhib Boards slide relative to each other as a result of horizontal shear. Elements are distorted as a resulting Vertical Shear Force. Dr. Ali Al-Gadhib Shear Formula Shear Formula Fx 0;
dA dA tdx 0 A A M dM M ydA ydA tdx 0 I I A A dM ydA tdx I A
Solving for , we get y 1 dM ydA It dx A Dr. Ali Al-Gadhib Where, dM V dx Q y * A* , VQ It y*
z First moment of inertia A* Shear Stress in Beams h A y b 2 * y 1 h y* y 22 * Q A y
Dr. Ali Al-Gadhib 1 h2 2 Q y b 2 4 max VQ Ib * 1.5 avg 1 h2 2
V y b 2 4 bh 3 12 b y 6V h 2 2 3 y bh 4 h/2 y z
h/2 b y max z max 3V 2A Dr. Ali Al-Gadhib Shear Stress failure in Beams Shear / Moment Capacity of a Beam
Most of the bending stress concentrated to the top and bottom. Then why use the same width ? Dr. Ali Al-Gadhib Flange carries bending stress Web carries shear stress Dr. Ali Al-Gadhib
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