Problem 1A

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[ ( )]

[ ( )]

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a) The dimension is increased b) The dimension is increased

c) The dimensions is decreased

Problem 1B

(a) The in-plane Mohr’s Circle is drawn. Axes are labeled, and the points X and Y are shown:

(b) The maximum in-plane shear stress is calculated:

√(

)

√(

)

And shown in the Mohr’s circle:

(c) A stress element oriented in the direction of the maximum in-plane shear stress is drawn. The

resulting stress components are indicated.

𝜏

𝜎 𝑌 (𝜎𝑦, ) 𝑋 ( 𝜎𝑦, )

𝜏

𝜎 𝑌 (𝜎𝑦, ) 𝑋 ( 𝜎𝑦, )

𝜏 𝑚𝑎𝑥𝑖𝑛 𝑝𝑙𝑎𝑛𝑒

𝜎𝑦

(d) The two out-of-plane Mohr’s circles are drawn.

(e) The absolute maximum shear stress is calculated:

𝜏𝑥𝑦′ 𝜏 𝑚𝑎𝑥

𝑖𝑛 𝑝𝑙𝑎𝑛𝑒 𝜎𝑦

𝜎𝑦′ 𝜎𝑎𝑣𝑔 5𝜎𝑦

𝜎𝑥′ 𝜎𝑎𝑣𝑔 5𝜎𝑦

𝜏

𝜎 𝑌 (𝜎𝑦, ) 𝑋 ( 𝜎𝑦, )

𝜏 𝑎𝑏𝑠𝑚𝑎𝑥

𝜎𝑦