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霍爾馬克的楊氏模量?jī)x(型號(hào):HO-ED-M-02)用于測(cè)量棒材的楊氏模量。楊氏模量是彈性材料的剛度的量度,并且是用于表征材料的量。根據(jù)材料的確切組成,它可能會(huì)發(fā)生很大變化。如果光束在其中點(diǎn)受力,則產(chǎn)生的凹陷將不會(huì)形成圓弧。這種彎曲稱為非均勻彎曲。如果梁的兩端都加載,則產(chǎn)生的高程將形成一個(gè)圓弧。這種彎曲稱為均勻彎曲。在均勻彎曲和不均勻彎曲中,使用兩種方法來測(cè)量鋼筋的楊氏模量。它們是銷和顯微鏡法和光學(xué)杠桿法。

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霍爾馬克的楊氏模量?jī)x(型號(hào):HO-ED-M-02)用于測(cè)量棒材的楊氏模量。楊氏模量是彈性材料的剛度的量度,并且是用于表征材料的量。根據(jù)材料的確切組成,它可能會(huì)發(fā)生很大變化。如果光束在其中點(diǎn)受力,則產(chǎn)生的凹陷將不會(huì)形成圓弧。這種彎曲稱為非均勻彎曲。如果梁的兩端都加載,則產(chǎn)生的高程將形成一個(gè)圓弧。這種彎曲稱為均勻彎曲。在均勻彎曲和不均勻彎曲中,使用兩種方法來測(cè)量鋼筋的楊氏模量。它們是銷和顯微鏡法和光學(xué)杠桿法。

在非均勻彎曲時(shí),梁(米標(biāo)尺)對(duì)稱地支撐在兩個(gè)刀刃上,并在其中心受力。*大凹陷發(fā)生在其中心。由于僅在梁的某個(gè)點(diǎn)施加載荷,因此這種彎曲在整個(gè)梁中都是不均勻的,因此將梁的彎曲稱為不均勻彎曲。

在均勻彎曲時(shí),將導(dǎo)條對(duì)稱地放置在兩個(gè)刀刃上。兩個(gè)重物吊架懸掛在離刀刃等距離的位置。權(quán)重被一一加起來,并得到相應(yīng)的讀數(shù)。根據(jù)這些讀數(shù),確定給定質(zhì)量的鋼筋中點(diǎn)的平均高度(e)。




Experiment Examples

    To find the Young's modulus of the material of a bar by uniform and non uniform bending using,

1. Pin and microscope method

1. Non uniform bending

Consider a bar of thickness d and breadth b is supported symmetrically between two knife edges at a distance l distance apart and loaded with a weight Mg at the center. The depression at the midpoint is given by,

Z = Mgl3 / 48 Y ( bd/ 12 )

The Young’s Modulus of the material of the bar

Y = Mg (l3 / z) / 4bd3

For a constant mass M, the quantity l3/z is a constant from which Y can be calculated.


2. Uniform bending

Consider a bar of thickness d and breadth b is supported symmetrically between two knife edges at a distance l distance apart and loaded with equal weights Mg at the ends at equal distance p from each knife edges. The elevation at the midpoint is given by,

Z = Mgpl2 / 8Y (bd3 / 12)

The Young’s Modulus of the material of the bar

Y = 3 Mgpl2 / 2bd3z



2. Optic Lever Method

1. Non uniform bending

According to the theory of non uniform bending, for a bar of thickness d and breadth b ; supported by two knife edges l distance apart, the depression at the midpoint due to a load M is given by,

Z = Mgl3 / 48 Y (bd3 / 12)

The Young’s Modulus of the material of the bar

Y = Mg (l3 / z) / 4bd3

If the optical lever, scale and laser arrangement are used for measuring the depression, the angle of twist of optic lever

Θ = z / x

Where x is the perpendicular distance to the legs of the optical lever

If y to the shift on the scale arranged at a distance D from the laser of the optical lever then

Θ = y / 2D

Z = xy / 2D

Thus,

Y = Mg / 2bd3x (Dl3 / y)

For a mass M, the quantity Dl3/y is a constant.



2. Uniform bending

Consider a bar of thickness d and breadth b is supported symmetrically between two knife edges at a distance l distance apart and loaded with equal weights Mg at the ends at equal distance p from each knife edges. The elevation at the midpoint is given by,

Z = Mgpl2 / 8Y (bd3 / 12)

The Young’s Modulus of the material of the bar

Y = 3Mg pl2 / 2bd3z

If the optical lever, scale and laser arrangement are used for measuring the depression, the angle of twist of optic lever

Θ = z / x

Where x is the perpendicular distance to the legs of the optical lever

If y to the shift on the scale arranged at a distance D from the laser of the optical lever then

Θ = y / 2D

Z = xy / 2D

Thus,

Y = 3Mgpl2 / bd3xy)






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