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# Strength of Materials I EGCE201 กำลังวัสดุ 1

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Strength of Materials I EGCE201 กำลังวัสดุ 1
Instructor: ดร.วรรณสิริ พันธ์อุไร (อ.ปู) ห้องทำงาน: 6391 ภาควิชาวิศวกรรมโยธา โทรศัพท์: 66(0) ต่อ 6391

Shearing Stress in Multiple Shafts
Static equilibrium must be satisfied. The vector of all applied torques = 0 TA+TB+TC+TD=0 The shearing stress at any point in the shaft is a function of the Internal torque on a plane containing the point. The maximum Stress is computed from Internal torque Radius of the shaft The polar moment of inertia

The shearing stress at a point on shaft
through which section 1 passes can only be defined once the internal torque is determined. From the free-body diagram, the internal torque at the section The shearing stress is given by

The shearing stress at a point on shaft
through which section 2 passes can only be defined once the internal torque is determined. From the free-body diagram, the internal torque at the section The shearing stress is given by

Angle of Twist in Multiple Shafts
For this shaft sections AB, BC, and CE will each have different Internal torque (FBD) Polar moment of inertia Shear Modulus Length The angle of twist of the end of a shaft consisting of N sections is expressed as

Relative Rotation fixed Both rotates Shaft AB
In some situations both ends of a shaft rotate. The angle of twist is the angle through which one end rotates w.r.t the other. fixed Both rotates Shaft AB

Shearing Stress on inclined planes

Shearing Stress on inclined planes

Statically Indeterminate Shafts
Both ends of the shaft are built in, leading to two reaction torques but one has only one moment equilibrium equation. The compatibility equation is the relative rotation! See example

Assuming a counterclockwise
torque is positive, summing moments about the axis of the shaft results in The total angle of twist of the shaft must be 0 since both ends are fixed.

โจทย์ตัวอย่างทบทวนความเค้นเฉือนภายใต้ภาระบิด

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5. continued

5. continued

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6. continued

6. continued

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